Question

If ∠D is a supplementary angle of ∠E and ∠F is a supplementary angle of ∠E, then which of the following statements is true?

Answer 1

Answer:

A) ∠D ≅ ∠F

Step-by-step explanation:

Supplementary angles : A pair of angles whose sum is 180° are called supplementary angles

We are given that ∠D is a supplementary angle of ∠E

So,$\angle D+\angle E = 180^{\circ} -----1$

We are also given that ∠F is a supplementary angle of ∠E

So,$\angle F+\angle E = 180^{\circ} ------2$

Find the value of ∠E form 1 and 2

From 1 : $\angle E = 180^{\circ}-\angle D$

From 2 : $\angle E = 180^{\circ}-\angle F$

So, $180^{\circ}-\angle D=180^{\circ}-\angle F$

$\angle D=\angle F$

So, Option A is true

Hence ∠D ≅ ∠F