Question

LOOK AT THE RIGHT-ANGLED TRIANGLE ABC THE SQUARE FITS EXACTLY IN THE TRIANGLE WORK OUT THE SIZES OF X, Y AND Z

Answer 1

Answer:

∠x = 90°

∠y = 58°

∠z = 32°

Step-by-step 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°