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?

Question 5 options:

A)

∠D ≅ ∠F

B)

∠D + ∠E ≅ ∠F

C)

∠E ≅ ∠F

D)

∠D ≅ ∠E

Answer 1

A) ∠D ≅ ∠F

Explanation:

Answer 2

A) ∠D ≅ ∠F

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