Question

4. In the following figure, AB II DG and BC || EF. Also, ZABC = 60°. Then find the measure of ZDEF​

Answer 1

Answer:

60°

Step-by-step explanation:

Given,

$AB\ // \ DE\\BC\ // \ EF$

∠ABC = 60°

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°.