Question

in the given figure AB =AC and and angle A is half of Angle B . find the measure of all the angles ​

Answer 1

Answer:

I hope it will help you

Answer 2

Answer:

∠A = 36°

∠B = 72°

∠C = 72°

Step-by-step explanation:

Given:

AB =AC (Thus, it is an Isoceles Triangle)

∠A is half of ∠B (means ∠A = 1/2∠B )

Sol:

∠B = AC ; ∠C = AB

∠B = ∠C (∵ Opposite angle of equal sides of an isosceles triangle are equal)

∠A + ∠B  + ∠C = 180° (∵ Angle Sum Property)

Substituting ∠B = ∠C

∠A + ∠B  + ∠B = 180°

∠A + 2∠B = 180°

Substituting  ∠A = 1/2∠B

1/2∠B + 2∠B = 180°

∠B/2 + 2∠B = 180° (we can write 1/2∠B as ∠B/2)

L.C.M = 2

∠B/2 + 4∠B/2 = 180°

5∠B/2 = 180°

5∠B = 180° x 2

∠B = 360°/5

∠B = 72°

∠C  = ∠B = 72°

∠A = 1/2∠B = 1/2(72°) = 36°