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If the angles of a quadrilateral are 4x, 3x + 10°, 2x + 10º and 4x + 15°, then find theangles. |
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Answer» hat:Angles of QUADRILATERAL ABCD are:→ ∠A = 4x∠B = 3x + 10°∠C = 2X + 10°∠D = 4x + 15°We KNOW that:SUM of all the four angles of a quadrilateral is EQUAL to 360°.i.e., ∠A + ∠B + ∠C + ∠D = 360°According to the question:→ 4x + 3x + 10° + 2x + 10º + 4x + 15° = 360°→ 4x + 3x + 2x + 4x + 10° + 10° + 15° = 360°→ 13x + 35° = 360°→ 13x = 360° - 35°→ 13x = 325°→ x = 325°/13→ x = 25°∴ Angles of quadrilateral ABCD are:∠A = 4x = 4 × 25° = 100°∠B = 3x + 10° = 3 × 25° + 10° = 75° + 10° = 85°∠C = 2x + 10° = 2 × 25° + 10° = 50° + 10° = 60°∠D = 4x + 15° = 4 × 25° + 15° = 100° + 15° = 115° |
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