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