In Fig. 5.31, PQ||ST. Then, the value of x + y is
a. 125°
b. 135°
c. 145°
d. 120°

Solution:

Given, PQ||ST.

We have to find the value of x + y.

Since PQ is parallel to ST, then PO will also be parallel to ST

Considering PO || ST intersected by a transversal OS,

The alternate interior angles are x and 85°

If two parallel lines are intersected by a transversal, each pair of alternate interior angles is equal.

By the above property,

x = 85°

We know that the sum of a linear pair of angles is always equal to 180 degrees.

y + 130° = 180°

y = 180° - 130°

y = 50°

Now, x + y = 85°+ 50°

= 135°

Therefore, x + y is 135°

✦ Try This: In figure, the two lines intersect each other. If ∠1 + ∠2 + ∠3 = 230°, then find the value of ∠1 and ∠4.

☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 5

NCERT Exemplar Class 7 Maths Chapter 5 Problem 40

In Fig. 5.31, PQ||ST. Then, the value of x + y is: a. 125°, b. 135°, c. 145°, d. 120°

Summary:

In Fig. 5.31, PQ||ST. Then, the value of x + y is 135°

☛ Related Questions:

• In Fig. 5.32, if PQ||RS and QR||TS, then the value a is: a. 95°, b. 90°, c. 85°, d. 75°
• If the sum of measures of two angles is 90°, then the angles are _________. Fill in the blanks to ma . . . .
• If the sum of measures of two angles is 180°, then the angles are _________. Fill in the blanks to m . . . .