Question

In triangle ABC , AB = AC , angle A = 2x° and angle B = x + 10°. Find the measures of all the angles of triangle ABC .

Answer 1

Refer the attachment

Answer 2

given: AB = AC , ∠A = 2x°, ∠B = x + 10°.

to find: all the angles of the triangle ABC

1. Since,

• A = 2x and B = x+10,

       we can find the third angle using angle sum property of a  triangle

• C = 180-(A+B)

putting values of A and B in C,

• C = 180-(2x + x + 10)

    2. since AB = AC,

• so ∠ABC = ∠ACB  (Angle same in front of same sides)

           ∴  x+10 = 180 - (2x + x + 10)

               4x + 20 = 180

               4x = 160

               x = 40°

calculating all the values using x, we get

     ∠A = 2x= 2(40) = 80°

     ∠B = x+10 = 90°

     ∠C = 10°

A = 80°, B = 90°, C = 10°