Find the value of the unknown ‘x’ in the following triangles.

1.	Find the value of the unknown ‘x’ in the following triangles.
Answer» i) In ΔABC ∠A + ∠B + ∠C = 180° (angle sum property) x° + 50° + 60° = 180° x° + 110° = 180° x° = 180° – 110° ii) In ΔPQR ∠P + ∠Q + ∠R = 180° (angle – sum property) 90° + 30° + x° = 180° 120° + x° – 180° x° = 180° – 120° ∴ x° = 60° iii) In ΔXYZ, ∠X + ∠Y + ∠Z = 180° (angle – sum property) 30°+110° + x° =180° 140° + x° = 180° x° = 180° – 140° ∴ x° = 40°

Answer»

i) In ΔABC

∠A + ∠B + ∠C = 180° (angle sum property)

x° + 50° + 60° = 180°

x° + 110° = 180°

x° = 180° – 110°

ii) In ΔPQR

∠P + ∠Q + ∠R = 180° (angle – sum property)

90° + 30° + x° = 180°

120° + x° – 180°

x° = 180° – 120°

∴ x° = 60°

iii) In ΔXYZ,

∠X + ∠Y + ∠Z = 180° (angle – sum property)

30°+110° + x° =180°

140° + x° = 180°

x° = 180° – 140°

∴ x° = 40°

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