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In each of the following triangles, find the value of x. |
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Answer» (i) Let ∠G = x By angle sum property we know that, ∠E + ∠F + ∠G = 180° 80° + 55° + x = 180° 135° + x = 180° x = 45° (ii) Let ∠M = x By angle sum property of triangles we have ∠M + ∠M + ∠O = 180° x + 96° + 22° = 180° x + 118° = 180° x = 180° – 118° = 62° (iii) Let ∠Z = (2x + 1)° and ∠Y = 90° By the sum property of triangles we have ∠x + ∠y + ∠z = 180° 29° + 90° + (2x + 1)° = 180° 119° + (2x + 1)° = 180° (2x + 1)° = 180° – 119° 2x + 1° = 61° 2x = 61° – 1° 2x = 60° x = \(\frac{60°}{2}\) x = 30° (iv) Let ∠J = x and ∠L = 3x. By angle sum property of triangles we have ∠J + ∠K + ∠L = 180° x + 112° + 3x = 180° 4x = 180° – 112° x = 68° x = \(\frac{68° }{4}\) x = 17° |
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