NCERT Exemplar solutions for Mathematics [English] Class 7 chapter 5 - Lines and Angles [Latest edition]

The angles between North and West and South and East are ______.

Angles between South and West and South and East are ______.

In the following figure, PQ is a mirror, AB is the incident ray and BC is the reflected ray. If ∠ABC = 46°, then ∠ABP is equal to ______.

If the complement of an angle is 79°, then the angle will be of ______.

Angles which are both supplementary and vertically opposite are ______.

The angle which makes a linear pair with an angle of 61° is of ______.

The angles x and 90° – x are ______.

The angles x – 10° and 190° – x are ______.

In the following figure, the value of x is ______.

In the following figure, if AB || CD, ∠APQ = 50° and ∠PRD = 130°, then ∠QPR is ______.

In the following figure, lines l and m intersect each other at a point. Which of the following is false?

If angle P and angle Q are supplementary and the measure of angle P is 60°, then the measure of angle Q is ______.

In the following figure, POR is a line. The value of a is ______.

In the following figure, POQ is a line. If x = 30°, then ∠QOR is ______.

The measure of an angle which is four times its supplement is ______.

In the following figure, the value of y is ______.

In the following figure, PA || BC || DT and AB || DC. Then, the values of a and b are respectively.

The difference of two complementary angles is 30°. Then, the angles are ______.

In the following figure, PQ || SR and SP || RQ. Then, angles a and b are respectively.

In the following figure, a and b are ______.

If two supplementary angles are in the ratio 1 : 2, then the bigger angle is ______.

In the following figure, ∠ROS is a right angle and ∠POR and ∠QOS are in the ratio 1 : 5. Then, ∠QOS measures ______.

Statements a and b are as given below:

a: If two lines intersect, then the vertically opposite angles are equal.

b: If a transversal intersects, two other lines, then the sum of two interior angles on the same side of the transversal is 180°.

Then ______.

For the following figure, statements p and q are given below:

p: a and b are forming a linear pair.

q: a and b are forming a pair of adjacent angles.

Then ______.

In the following figure, ∠AOC and ∠BOC form a pair of ______.

In the following figure, the value of a is ______.

In the following figure, if QP || SR, the value of a is ______.

In which of the following figures, a and b are forming a pair of adjacent angles?

In a pair of adjacent angles,

1. vertex is always common, 
2. one arm is always common, and 
3. uncommon arms are always opposite rays
   Then ______.

In the following figure, lines PQ and ST intersect at O. If ∠POR = 90° and x : y = 3 : 2, then z is equal to ______.

In the following figure, POQ is a line, then a is ______.

Vertically opposite angles are always ______.

In the following figure, a = 40°. The value of b is ______.

If an angle is 60° less than two times of its supplement, then the greater angle is ______.

In the following figure, PQ || RS. If ∠1 = (2a + b)° and ∠6 = (3a – b)°, then the measure of ∠2 in terms of b is ______.

In the following figure, PQ || RS and a : b = 3 : 2. Then, f is equal to ______.

In the following figure, line l intersects two parallel lines PQ and RS. Then, which one of the following is not true?

In the following figure, which one of the following is not true?

In the following figure, which of the following is true?

In the following figure, PQ || ST. Then, the value of x + y is ______.

In the following figure, if PQ || RS and QR || TS, then the value a is ______.

If sum of measures of two angles is 90°, then the angles are ______.

If the sum of measures of two angles is 180°, then they are ______.

A transversal intersects two or more than two lines at ______ points.

If a transversal intersects two parallel lines, then sum of interior angles on the same side of a transversal is ______.

If a transversal intersects two parallel lines, then alternate interior angles have one common ______.

If a transversal intersects two parallel lines, then corresponding angles are on the ______ side of the transversal.

If a transversal intersects two parallel lines, then alternate interior angles are on the ______ side of the transversal.

Two lines in a plane which do not meet at a point anywhere are called ______ lines.

Two angles forming a ______ pair are supplementary.

The supplement of an acute is always ______ angle.

The supplement of a right angle is always ______ angle.

The supplement of an obtuse angle is always ______ angle.

In a pair of complementary angles, each angle cannot be more than ______ .

An angle is 45°. Its complementary angle will be ______.

An angle which is half of its supplement is of ______.

Two right angles are complementary to each other.

One obtuse angle and one acute angle can make a pair of complementary angles.

Two supplementary angles are always obtuse angles.

Two right angles are always supplementary to each other.

One obtuse angle and one acute angle can make a pair of supplementary angles.

Both angles of a pair of supplementary angles can never be acute angles.

Two supplementary angles always form a linear pair.

Two angles making a linear pair are always supplementary.

Two angles making a linear pair are always adjacent angles.

Vertically opposite angles form a linear pair.

Interior angles on the same side of a transversal with two distinct parallel lines are complementary angles.

Vertically opposite angles are either both acute angles or both obtuse angles.

A linear pair may have two acute angles.

An angle is more than 45°. Its complementary angle must be less than 45°.

Two adjacent angles always form a linear pair.

Write down the pair of adjacent angles shown in the following figure:

Write down the pair of adjacent angles shown in the following figure:

Write down the pair of adjacent angles shown in the following figure:

Write down the pair of adjacent angles shown in the following figure:

In the following figure, write, if any, (i) each pair of vertically opposite angles, and (ii) each linear pair.

In the following figure, write, if any, (i) each pair of vertically opposite angles, and (ii) each linear pair.

In the following figure, write, if any, (i) each pair of vertically opposite angles, and (ii) each linear pair.

In the following figure, write, if any, (i) each pair of vertically opposite angles, and (ii) each linear pair.

Name the pairs of supplementary angles in the following figure:

Name the pairs of supplementary angles in the following figure:

Name the pairs of supplementary angles in the following figure:

In the following figure, PQ || RS, TR || QU and ∠PTR = 42°. Find ∠QUR.

The drawings below (Figure), show angles formed by the goalposts at different positions of a football player. The greater the angle, the better chance the player has of scoring a goal. For example, the player has a better chance of scoring a goal from Position A than from Position B.

In Parts (a) and (b) given below it may help to trace the diagrams and draw and measure angles.

1. Seven football players are practising their kicks. They are lined up in a straight line in front of the goalpost [Figure]. Which player has the best (the greatest) kicking angle?
2. Now the players are lined up as shown in figure. Which player has the best kicking angle?
3. Estimate atleast two situations such that the angles formed by different positions of two players are complement to each other.

The sum of two vertically opposite angles is 166°. Find each of the angles.

In the following figure, l || m || n. ∠QPS = 35° and ∠QRT = 55°. Find ∠PQR.

In the following figure, P, Q and R are collinear points and TQ ⊥ PR, name; pair of complementary angles.

In the following figure, P, Q and R are collinear points and TQ ⊥ PR, name; two pairs of supplementary angles.

In the following figure, P, Q and R are collinear points and TQ ⊥ PR, name; four pairs of adjacent angles.

In the following figure, OR ⊥ OP. Name all the pairs of adjacent angles.

In the following figure, OR ⊥ OP. Name all the pairs of complementary angles.

If two angles have a common vertex and their arms form opposite rays (Figure), Then, how many angles are formed?

If two angles have a common vertex and their arms form opposite rays (Figure), Then, how many types of angles are formed?

If two angles have a common vertex and their arms form opposite rays (Figure), Then, write all the pairs of vertically opposite angles.

In the following figure are the following pairs of angles adjacent? Justify your answer.

In the following figure, are the following pairs of angles adjacent? Justify your answer.

In the following figure, are the following pairs of angles adjacent? Justify your answer.

In the following figure, are the following pairs of angles adjacent? Justify your answer.

In the following figure, write all the pairs of supplementary angles.

What is the type of other angle of a linear pair if one of its angle is acute?

What is the type of other angle of a linear pair if one of its angles is obtuse?

What is the type of other angle of a linear pair if one of its angles is right?

Can two acute angles form a pair of supplementary angles? Give reason in support of your answer.

Two lines AB and CD intersect at O (see the figure). Write all the pairs of adjacent angles by taking angles 1, 2, 3, and 4 only.

If the complement of an angle is 62°, then find its supplement.

A road crosses a railway line at an angle of 30° as shown in the following. Find the values of a, b and c.

The legs of a stool make an angle of 35° with the floor as shown in the following figure. Find the angles x and y.

Iron rods a, b, c, d, e and f are making a design in a bridge as shown in the following figure, in which a || b, c || d, e || f. Find the marked angles between

1. b and c
2. d and e
3. d and f
4. c and f

Amisha makes a star with the help of line segments a, b, c, d, e and f, in which a || d, b || e and c || f. Chhaya marks an angle as 120° as shown in the following figure and asks Amisha to find the ∠x, ∠y and ∠z. Help Amisha in finding the angles.

In the following figure, AB || CD, AF || ED, ∠AFC = 68° and ∠FED = 42°. Find ∠EFD.

In the following figure, OB is perpendicular to OA and ∠BOC = 49°. Find ∠AOD.

Three lines AB, CD and EF intersect each other at O. If ∠AOE = 30° and ∠DOB = 40° (Figure), find ∠COF.

Measures (in degrees) of two complementary angles are two consecutive even integers. Find the angles.

If a transversal intersects two parallel lines, and the difference of two interior angles on the same side of a transversal is 20°, find the angles.

Two angles are making a linear pair. If one of them is one-third of the other, find the angles.

Measures (in degrees) of two supplementary angles are consecutive odd integers. Find the angles.

In the following figure, AE || GF || BD, AB || CG || DF and ∠CHE = 120°. Find ∠ABC and ∠CDE.

In the following figure, find the value of ∠BOC, if points A, O and B are collinear.

In the following figure, if l || m, find the values of a and b.

In the following figure, l || m and a line t intersects these lines at P and Q, respectively. Find the sum 2a + b.

In the following figure, QP || RS. Find the values of a and b.

In the following figure, PQ || RT. Find the value of a + b.

In the following figure, PQ, RS and UT are parallel lines. If c = 57° and `a = c/3`, find the value of d.

In the following figure, PQ, RS and UT are parallel lines. If c = 75° and `a = 2/5 c`, find b.

In the following figure, AB || CD. Find the reflex ∠EFG.

In the following figure, two parallel lines l and m are cut by two transversals n and p. Find the values of x and y.

In the following figure, l, m and n are parallel lines, and the lines p and q are also parallel. Find the values of a, b and c.

In the following figure, state which pair of lines are parallel. Give reason.

In the following figure, examine whether the following pairs of lines are parallel or not:

EF and GH

In the following figure, examine whether the following pairs of lines are parallel or not:

AB and CD

In the following figure, find out which pair of lines are parallel:

In the following figure, show that

1. AB || CD
2. EF || GH

In the following figure, two parallel lines l and m are cut by two transversals p and q. Determine the values of x and y.