Question

11. In the following figure, AB||DG and BC||EF. Also ∠ABC=60°, Then the measure of ∠DEF is
30°
60°

45°
120°

Answer 1

Given:

AB||DG and BC||EF.

Measure of ∠ABC = 60°

To find:

The measure of ∠DEF

Solution:

Given that, AB||DG. Let BC be the transversal. And also given that

∠ABC = 60°. When two lines are parallel and they are cut by a transversal that intersects them at two points, then the angles formed at the points of intersection are equal, i.e., corresponding angles are equal. Here, the angle corresponding to ∠ABC is ∠DGC.

Hence, ∠DGC = 60°.

Given that, BC||EF. Let DE be the transversal. Then,

∠DGC = ∠DEF    (∵ Corresponding angles are equal)

∠DGC = 60°

Hence, ∠DEF = 60°.

Thus, option (b) is the correct answer.

The measure of ∠DEF = 60°. Option (b) is the correct answer.