Advertisements
Advertisements
Question
In the given figure, AB and CD are parallel lines and transversal EF intersects them at Pand Q respectively. If ∠APR = 25°, ∠RQC = 30° and ∠CQF = 65°, then
Options
x = 55°, y = 40°
x = 50°, y = 45°
x = 60°, y = 35°
x = 35°, y = 60°
Advertisements
Solution
In the given figure and AB|| CD , ∠APR = 25°, ∠RQC = 30V , and ∠CQF = 65°
We need to find the value of x and y
Here, we draw a line ST parallel to AB, i.e AB || ST
Also, using the property, “two lines parallel to the same line are parallel to each other”
As,
AB || ST
AB || CD
Thus, CD || ST
Now, AB || ST and EF is the transversal, so using the property, ”alternate interior angles are equal”, we get,
∠APR = ∠PRT
∠PRT = 25° .......... (1)
Similarly, CD || ST and EF is the transversal
∠QRT = ∠RQC
∠QRT = 30° .......(2)
Adding (1) and (2), we get
∠PRT + ∠QRT = 25° + 30°
x = 55°
Further,FPE is a straight line
Applying the property, angles forming a linear pair are supplementary
∠CQF + ∠CQR + ∠RQP = 180°
65° + 30° + ∠RQP = 180°
∠RQP = 180° - 95°
∠RQP = 85°
Also, applying angle sum property of the triangle
In ΔPRQ
∠RPQ + 55° + 85° = 180°°
140° + y = 180°
y = 180° - 140°
y = 40°
Thus, x = 55° and y = 40°
APPEARS IN
RELATED QUESTIONS
ABC is an isosceles triangle in which altitudes BE and CF are drawn to equal sides AC and AB respectively (see the given figure). Show that these altitudes are equal.
ΔABC is an isosceles triangle in which AB = AC. Side BA is produced to D such that AD = AB (see the given figure). Show that ∠BCD is a right angle.
In Figure AB = AC and ∠ACD =105°, find ∠BAC.
If the base of an isosceles triangle is produced on both sides, prove that the exterior angles so formed are equal to each other.
If the base of an isosceles triangle is produced on both sides, prove that the exterior angles so formed are equal to each other.
ABC is a triangle in which BE and CF are, respectively, the perpendiculars to the sides AC and AB. If BE = CF, prove that ΔABC is isosceles
Fill the blank in the following so that the following statement is true.
Angle opposite to equal sides of a triangle are .....
Fill the blank in the following so that the following statement is true.
If altitudes CE and BF of a triangle ABC are equal, then AB = ....
Which of the following statements are true (T) and which are false (F)?
Sum of the three sides of a triangle is less than the sum of its three altitudes.
Which of the following statements are true (T) and which are false (F)?
Sum of any two sides of a triangle is greater than twice the median drawn to the third side.
Which of the following statements are true (T) and which are false (F)?
Sum of any two sides of a triangle is greater than the third side.
Which of the following statements are true (T) and which are false (F)?
If two angles of a triangle are unequal, then the greater angle has the larger side opposite to it.
Fill in the blank to make the following statement true.
The sum of three altitudes of a triangle is ..... than its perimeter.
In the given figure, the sides BC, CA and AB of a Δ ABC have been produced to D, E and F respectively. If ∠ACD = 105° and ∠EAF = 45°, find all the angles of the Δ ABC.
If the angles A, B and C of ΔABC satisfy the relation B − A = C − B, then find the measure of ∠B.
In the given figure, what is z in terms of x and y?
In the given figure, what is y in terms of x?
Two sides of a triangle are of lengths 5 cm and 1.5 cm. The length of the third side of the triangle cannot be ______.
Find all the angles of an equilateral triangle.
In a triangle ABC, D is the mid-point of side AC such that BD = `1/2` AC. Show that ∠ABC is a right angle.
