Question

Look at the right-angled triangle ABC.

A
320
B
С
The square fits exactly inside the triangle.
Work out the sizes of angles x, y and z.​

Answer 1

∠x = 90°

∠y = 58°

∠z = 32°

Explanation:

The dimensions of the angles given are;

∠B = 32°

Whereby ΔABC is a right-angled triangle, and the square fits at angle A, we have;

∠A = 90°

∴ ∠B + ∠C = 90° which gives

32° + ∠C = 90°

∠C = 58°

∠x + Interior angle of the square = 180° (Sum of angles on a straight line)

∴ ∠x + 90° = 180°

Hence;

∠x = 90°

∠x + ∠y + 32° = 180° (Sum of angles in a triangle)

∴ 90° + ∠y + 32° = 180°

∠y = 180 - 90° - 32° = 58°

∠y + ∠z + Interior angle of the square = 180° (Sum of angles on a straight line)

58° + ∠z +90° = 180°

∴ ∠z = 32°

∠x = 90°

∠y = 58°

∠z = 32°