Question

In the figure∠BAC= 55°, then find∠AED​

Answer 1

Answer:

I think answer is the 135

Answer 2

Answer:

Given:

∠B = 55°

AD is perpendicular to BC.

AE is the angle bisector of ∠DAB.

Concept:

The sum of all angles of a triangle is 180.

The angle bisector is a line that divides the angle into two equal parts.

Calculation:

F1 Amar Kumar Anil 19-05.21 D12

In ΔABD,

∠ABD + ∠BAD + ∠ADB = 180°

⇒ 55° + ∠BAD + 90° = 180

⇒ ∠BAD = 180 - 145

⇒ ∠BAD = 35°

According to the question,

∠EAD = ∠BAD/2

⇒ ∠EAD = 35/2

⇒ ∠EAD = 17.5°

Now, In ΔADE we can write,

∠ADE + ∠AED + ∠EAD = 180

⇒ 90° + 17.5° + ∠AED = 180

⇒ ∠AED = 180° - 107.5°

⇒ ∠AED = 72.5°

∴ The measure of ∠AED is 72.5°.

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