Question

The vertex angle of an isosceles triangle is 3 times the sum of its base angles. Find each angle.

Answer 1

Let the base angles = x

Sum of base angles = x+x = 2x

vertex angle is 3 times the sum of its base angles.

So vertex angle = 3×2x = 6x

Sum of angles = 180

=> x + x + 6x = 180

=> 8x = 180

=> x = 180/8

=> x = 22.5°

6x = 22.5 × 6 = 135°

Angles are 22.5°, 22.5° and 135°

Answer 2

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⏩Let the angles = y

⏩Sum of base angles = y+y = 2y

⏩vertex angle is 3 times the sum of its base angles.

•°• vertex angle = 3×2y = 6y

⏩Sum of angles = 180

⏩y + y + 6y = 180

⏩8y = 180

⏩ y = 180/8

⏩y = 22.5°

⏩6y = 22.5 × 6 = 135°

Angles are 22.5°, 22.5° and 135°


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