###### Advertisements

###### Advertisements

In the given figure, sides QP and RQ of ΔPQR are produced to points S and T respectively. If ∠SPR = 135º and ∠PQT = 110º, find ∠PRQ.

###### Advertisements

#### Solution

It is given that,

∠SPR = 135º and ∠PQT = 110º

∠SPR + ∠QPR = 180º (Linear pair angles)

⇒ 135º + ∠QPR = 180º

⇒ ∠QPR = 45º

Also, ∠PQT + ∠PQR = 180º (Linear pair angles)

⇒ 110º + ∠PQR = 180º

⇒ ∠PQR = 70º

As the sum of all interior angles of a triangle is 180º, therefore, for ΔPQR,

∠QPR + ∠PQR + ∠PRQ = 180º

⇒ 45º + 70º + ∠PRQ = 180º

⇒ ∠PRQ = 180º − 115º

⇒ ∠PRQ = 65º

#### APPEARS IN

#### RELATED QUESTIONS

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

In the given figure, if lines PQ and RS intersect at point T, such that ∠PRT = 40º, ∠RPT = 95º and ∠TSQ = 75º, find ∠SQT.

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 unknown x 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

Observe the figure and find the value of ∠A + ∠N + ∠G + ∠L + ∠E + ∠S

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

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

In ∆DEF, ∠F = 48°, ∠E = 68° and bisector of ∠D meets FE at G. Find ∠FGD

If one of the angles of a triangle is 130°, then the angle between the bisectors of the other two angles can be ______.

How many triangles can be drawn having its angles as 45°, 64° and 72°? Give reason for your answer.

How many triangles can be drawn having its angles as 53°, 64° and 63°? Give reason for your answer.

Two adjacent angles are equal. Is it necessary that each of these angles will be a right angle? Justify your answer.

The angles of a triangle are in the ratio 2:3:4. Find the angles of the triangle.

Prove that a triangle must have atleast two acute angles.

In the figure, ∠Q > ∠R, PA is the bisector of ∠QPR and PM ⊥ QR. Prove that ∠APM = `1/2` (∠Q – ∠R).

In an isosceles triangle, one angle is 70°. The other two angles are of ______.

- 55° and 55°
- 70° and 40°
- any measure

In the given option(s) which of the above statement(s) are true?

In the given figure, PB = PD. The value of x is ______.

If two angles of a triangle are 60° each, then the triangle is ______.

In ∆PQR, if PQ = QR and ∠Q = 100°, then ∠R is equal to ______.

If two triangles are congruent, then the corresponding angles are equal.

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

I have three sides. One of my angle measures 15°. Another has a measure of 60°. What kind of a polygon am I? If I am a triangle, then what kind of triangle am I?

The angles of a triangle are in the ratio 2:3:5. Find the angles.

In ΔPQR, if 3∠P = 4∠Q = 6∠R, calculate the angles of the triangle.