Question

What will replace x?

Answer 1

We can Notice that : Triangle ABF is an Isosceles Triangle

⇒ ∠ABF = ∠AFB

Let us take ∠ABF = ∠AFB = p

We know that : Sum of Angles in a Triangle = 180°

⇒ ∠ABF + ∠AFB + ∠BAF = 180°

⇒ p + p + 36° = 180°

⇒ 2p + 36° = 180°

⇒ 2p = 144°

⇒ p = 72°

⇒ ∠ABF = ∠AFB = 72°

We can Notice that : Sum of Angles (∠AFB , ∠AFE , ∠EFG) = 180°

⇒ ∠AFB + ∠AFE + ∠EFG = 180°

⇒ 72° + 58° + ∠EFG = 180°

⇒ 130° + ∠EFG = 180°

⇒ ∠EFG = 50°

We can Notice that : Triangle FEG is an Isosceles Triangle

⇒ ∠FEG = ∠FGE

Let us take ∠FEG = ∠FGE = q

⇒ ∠FEG + ∠FGE + ∠EFG = 180°

⇒ q + q + 50° = 180°

⇒ 2q + 50° = 180°

⇒ 2q = 130°

⇒ q = 65°

⇒ ∠FEG = ∠FGE = 65°

We can Notice that ∠FGE and ∠x form a Linear Pair (180°)

⇒ ∠FGE + ∠x = 180°

⇒ 65° + ∠x = 180°

⇒ ∠x = 115°

$\heartsuit$  Welcome to December!  $\heartsuit$

Answer 2

hey mate your answer is in the attachment.....