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Question Find the measures of the angles of these triangles.
(i) In ∆ABC, AB = AC [Given] ∠B = ∠C [Angles opposite to equal sides in a triangle are equal] So ∠B = y + 15 ∠A + ∠B + ∠C = 180° [Angle sum property of ∆] ⇒ y + y + 15 + y + 15 = 180° ⇒ 3y + 30 = 180° ⇒ 3y = 180 – 30 ⇒ 3y = 150 ⇒ y = 50 ∠A = 50°, ∠B = 50° + 15° = 65°, and ∠C = 50° + 15° = 65° (ii) In ∆ABC, ∠A + ∠B + ∠C = 180° [Sum of angles of a triangle is 180°] ⇒ x + x – 10 + x + 10 = 180° ⇒ 3x = 180° ⇒ x = 60° ∠A = 60°, ∠B = 60° – 10° = 50° and ∠C = 60° + 10° = 70°