Question

Find the measure of the third angle of a triangle:

(i) ∠A = 60°, ∠B = 60°

(ii) ∠A = 70°, ∠B = 80°

(iii) ∠A = 90°, ∠B = 10°

(iv) ∠A = 95°, ∠B = 25°

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Answer 1

Answer:

(1) ka 60°

(2) ka 30°

(3) ka 80°

(4) ka 60°

Step-by-step explanation:

Sum of all three angles is equal to 180°

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Answer 2

• (i) ∠A = 60°, ∠B = 60°

Answer (i) ∠C = 60°

∠A + ∠B + ∠C = 180°

⇒ 60° + 60° + ∠C = 180°

⇒ (120°) + ∠C = 180°

⇒ ∠C = 180° - 120°

∴ ∠C = 60°

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• (ii) ∠A = 70°, ∠B = 80°

Answer (ii) ∠C = 30°

∠A + ∠B + ∠C = 180°

⇒ 70° + 80° + ∠C = 180°

⇒ (150°) + ∠C = 180°

⇒ ∠C = 180° - 150°

∴ ∠C = 30°

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• (iii) ∠A = 90°, ∠B = 10°

Answer (iii) ∠C = 80°

∠A + ∠B + ∠C = 180°

⇒ 90° + 10° + ∠C = 180°

⇒ (100°) + ∠C = 180°

⇒ ∠C = 180° - 100°

∴ ∠C = 80°

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• (iv) ∠A = 95°, ∠B = 25°

Answer (iv) ∠C = 60°

∠A + ∠B + ∠C = 180°

⇒ 95° + 25° + ∠C = 180°

⇒ (120°) + ∠C = 180°

⇒ ∠C = 180° - 120°

∴ ∠C = 60°

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More Information:

• In a triangle the sum of all the three interior angles = 180° [Angle sum property of a triangle.]
• If all the interior angles of a triangle = 60° then the triangle is an equilateral triangle. All three sides are equal in length.