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in Triangles by (65.5k points)

Find the value of the unknown x in the following diagrams :

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Best answer

(i) ∠A + ∠B + ∠C = 180°

x° + 50° + 60° = 180° 

(By Angle sum property of a triangle)

∠x + 110° = 180°

∠x = 180° – 110°

∠x = 70°

(ii) ∠P + ∠Q + ∠R = 180°

90° + 30° + ∠x = 180° 

(By Angle sum property of a triangle)

120° + ∠x = 180°

∠x = 180° – 120° = 60°

(iii) ∠X + ∠Y + ∠Z = 180°

30° + 110° + ∠x = 180° 

(By Angle sum property of a triangle)

140° + ∠x = 180°

∴ ∠x = 180° – 140° = 40°

(iv) 50° + x + x = 180°

50° + 2x = 180°

(By Angle sum property of a triangle)

2x = 180° – 50° = 130°

x = \(\frac{180^o}{2}\)

∴ ∠x = 60°

(v) x + x + x = 180°

(By Angle sum property of a triangle)

3x = 180°

x = \(\frac{180^o}{2}\)

∴ x = 60°

(vi) x + 2x + 90° = 180° 

(ByAngle sum property of a triangle)

3x = 180°

x = \(\frac{180^o}{3} = 60^o\)

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