Question

In triangle ABC, Angle A is twice the size of angle B, angle C measures 20 degrees less than angle A, find the measurements of a,b, and c

Answer 1

I assume a, b, and c are the measures of the angles A, B, and C themselves. (If you meant lengths of the sides opposite these angles, this would be impossible.)

The interior angles to any triangle sum to 180° in measure, so

A + B + C = 180°

Now,

• A is twice the size of B, so A = 2B or B = A/2

• C measures 20° less than A, so C = A - 20°

Substitute these into the first equation and solve for A :

A + A/2 + (A - 20°) = 180°

5/2 A - 20° = 180°

5/2 A = 200°

A = 80°

Solve for B and C :

B = 80°/2

B = 40°

C = 80° - 20°

C = 60°