# In Fig. 6.42, if lines PQ and RS intersect at point T, such that ∠PRT = 40°, ∠RPT = 95° and ∠TSQ = 75°, find ∠SQT.

**Solution:**

Given: ∠PRT = 40° , ∠RPT = 95° and ∠TSQ = 75°

To find: ∠SQT

We know that when two lines intersect each other at a point then there are two pairs of vertically opposite angles formed that are equal.

According to the angle sum property of a triangle, sum of the interior angles of a triangle is 360°.

In △PRT,

∠PTR + ∠PRT + ∠RPT = 180° [Angle sum property of a triangle]

∠PTR + 40° + 95° = 180°

∠PTR = 180° - 135°

∠PTR = 45°

Now,

∠QTS = ∠PTR [Vertically opposite angles]

∠QTS = 45°...... (i)

In △TSQ,

∠QTS + ∠TSQ + ∠SQT = 180° [Angle sum property of a triangle]

45° + 75° + ∠SQT = 180° [From (i)]

∠SQT = 180° - 120°

∠SQT = 60°

Hence, ∠SQT = 60°

**☛ Check: **NCERT Solutions for Class 9 Maths Chapter 6

**Video Solution:**

## In Fig. 6.42, if lines PQ and RS intersect at point T, such that ∠PRT = 40°, ∠RPT = 95° and ∠TSQ = 75°, find ∠SQT.

NCERT Maths Solutions Class 9 Chapter 6 Exercise 6.3 Question 4

**Summary:**

In Fig. 6.42, if lines PQ and RS intersect at point T, such that ∠PRT = 40°, ∠RPT = 95°, and ∠TSQ = 75°, then ∠SQT = 60°.

**☛ Related Questions:**

- In Fig. 6.39, sides QP and RQ of ∆PQR are produced to points S and T respectively. If ∠SPR =135° and ∠PQT = 110°, find ∠PRQ.
- In Fig. 6.40, ∠X = 62°, ∠XYZ = 54°. If YO and ZO are the bisectors of ∠XYZ and ∠XZY respectively of ∠XYZ, find ∠OZY and ∠YOZ.
- In Fig. 6.41, if AB || DE, ∠BAC = 35° and ∠CDE = 53°, find ∠DCE.
- In Fig. 6.43, if PQ ⊥ PS, PQ || SR, ∠SQR = 28° and ∠QRT = 65° then find the values of x and y.

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