Question

In ∆XYZ, if ∠X : ∠Z is 5 : 4 and ∠Y = 72°. Find ∠X and ∠Z

Answer 1

Given in ∆XYZ, ∠X : ∠Z = 5 : 4

Let ∠X = 5x, and ∠Z = 4x given ∠Y = 72°

By the angle sum property of triangle sum of three angles of a triangle is 180°.

∠X + ∠Y + ∠Z = 180°

5x + 72 + 4x = 180°

5x + 4x = 180° – 72°

9x = 108°

x = `(108^circ)/9` = 12°

∠X = 5x = 5 × 12° = 60°

∠Z = 4x = 4 × 12° = 48°

∴ ∠X = 60°

∠Z = 48°