###### Advertisements

###### Advertisements

In the given figure, if PQ ⊥ PS, PQ || SR, ∠SQR = 28º and ∠QRT = 65º, then find the values of *x* and *y*.

###### Advertisements

#### Solution

It is given that PQ || SR and QR is a transversal line.

∠PQR = ∠QRT (Alternate interior angles)

*x* + 28º = 65º

*x *= 65º − 28º

*x* = 37º

By using the angle sum property for ΔSPQ, we obtain

∠SPQ + *x* + *y* = 180º

90º + 37º + *y* = 180º

*y* = 180º − 127º

*y *= 53º

*∴x* = 37º and *y* = 53º

#### APPEARS IN

#### RELATED QUESTIONS

In the given figure, ∠X = 62º, ∠XYZ = 54º. If YO and ZO are the bisectors of ∠XYZ and ∠XZY respectively of ΔXYZ, find ∠OZY and ∠YOZ.

In the given figure, if AB || DE, ∠BAC = 35º and ∠CDE = 53º, find ∠DCE.

In the given figure, the side QR of ΔPQR is produced to a point S. If the bisectors of ∠PQR and ∠PRS meet at point T, then prove that ∠QTR = 1/2∠QPR.

**Find the value of the unknowns x and y in the following diagram:**

**Find the value of the unknowns x and y in the following diagram:**

**Find the value of the unknowns x and y in the following diagram:**

In the following triangle, find the value of x

In the following triangle, find the value of x

In the following triangle, find the value of x

In the following triangle, find the value of x

In the following triangle, find the value of x

In ∆XYZ, if ∠X : ∠Z is 5 : 4 and ∠Y = 72°. Find ∠X and ∠Z

In a right angled triangle ABC, ∠B is right angle, ∠A is x + 1 and ∠C is 2x + 5. Find ∠A and ∠C

In a right angled triangle MNO, ∠N = 90°, MO is extended to P. If ∠NOP = 128°, find the other two angles of ∆MNO

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

If ∆MNO ≅ ∆DEF, ∠M = 60° and ∠E = 45° then find the value of ∠O

If one angle of a triangle is equal to the sum of the other two angles, then the triangle is ______.

Angles of a triangle are in the ratio 2:4:3. The smallest angle of the triangle is ______.

Can a triangle have all angles less than 60°? Give reason for your answer.

Can a triangle have two obtuse angles? Give reason for your answer.

A triangle ABC is right-angled at A. L is a point on BC such that AL ⊥ BC. Prove that ∠BAL = ∠ACB.

Prove that through a given point, we can draw only one perpendicular to a given line.

Prove that a triangle must have atleast two acute angles.

If one angle of a triangle is equal to the sum of the other two angles, the triangle is ______.

The measure of three angles of a triangle are in the ratio 5:3:1. Find the measures of these angles.

In triangle XYZ, the measure of angle X is 30° greater than the measure of angle Y and angle Z is a right angle. Find the measure of ∠Y.

In a triangle ABC, the measure of angle A is 40° less than the measure of angle B and 50° less than that of angle C. Find the measure of ∠A.

In a right-angled triangle if an angle measures 35°, then find the measure of the third angle.

Each of the two equal angles of an isosceles triangle is four times the third angle. Find the angles of the triangle.

The angles of a triangle are arranged in descending order of their magnitudes. If the difference between two consecutive angles is 10°, find the three angles.