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+1 vote
1.0k views
in Mathematics by (30.0k points)
Given : In quadrilateral ABCD ; ∠C = 64°, ∠D = ∠C – 8° ; ∠A = 5(a+2)° and ∠B = 2(2a+7)°.

Calculate ∠A.

1 Answer

+2 votes
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Best answer

∠C = 64° (Given)

∠D = ∠C – 8° = 64°- 8° = 56°

∠A = 5(a+2)°

∠B = 2(2a+7)°

Now ∠A + ∠B + ∠C + ∠D = 360°

5(a+2)° + 2(2a+7)° + 64° + 56° = 360°

5a + 10 + 4a + 14° + 64° + 56° = 360°

9a + 144° = 360°

9a = 360° – 144°

9a = 216°

a = 24°

∠A = 5 (a + 2) = 5(24+2) = 130°

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