In Fig. 6.35, QP || RT. Find the values of x and y.

Solution:

Given, PQR is a triangle.

Also, QP || RT

We have to find the values of x and y.

Since QP || RT, the alternate interior angles are equal.

So, ∠QPR = ∠PRT

x = 70°

Angle sum property of a triangle states that the sum of all three interior angles of a triangle is always equal to 180 degrees.

By angle sum property,

∠P + ∠Q + ∠R = 180°

x + 30° + y = 180°

70° + 30° + y = 180°

100° + y = 180°

y = 180° - 100°

y = 80°

Therefore, the values of x and y are 70° and 80°.

✦ Try This: Find the value of x and y.

☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 6

NCERT Exemplar Class 7 Maths Chapter 6 Problem 118

In Fig. 6.35, QP || RT. Find the values of x and y.

Summary:

In Fig. 6.35, QP || RT. The values of x and y are 70° and 80°.

☛ Related Questions:

• Find the measure of ∠A in Fig. 6.36
• 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 . . . .