Two angles of a triangle are same and the third angle is 15° more than the each angle, then find the measure of each angle.
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Two angles of a triangle are same and the third angle is 15° more than the each angle, then find the measure of each angle.

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Solution —

Let the two equal angles be x, then the third angle = x + 15°

∵The total measure of the three angles of a triangle = 180°

 ∴ ∠A + ∠B + ∠C =180°

⇒ x + 15° + x + x = 180°

⇒ 3x + 15° = 180°

⇒ 3x = 180° - 15° = 165°

∴ x = 165° / 3 = 55°

∴ The third angle = x + 15°

                            = 55° + 15°

                            = 70°

Hence, the angles are 55° and 70°

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