Question

Given : In quadrilateral ABCD ; ∠C = 64°, ∠D = ∠C – 8° ; ∠A = 5(a + 2)° and ∠B = 2(2a + 7)°. Calculate ∠A.

Answer 1

$<b>Sum of all angles of quadrilateral = 360°</b>$

•°•

∠A + ∠B + ∠C + ∠D = 360°

5 ( a + 2 )° + 2 ( 2a + 7 )° + 64° + ∠C - 8° = 360°

5a + 10° + 4a + 14° + 64° + 64° - 8 = 360°

5a + 4a + 10° + 14° + 64° + 64° - 8° = 360°

9a + 144° = 360°

9a = 360° - 144°

9a = 216°

a = 216° / 9

a = 24°

Now,

∠A = 5 ( a + 2 )°

∠A = 5 ( 24 + 2 )°

$<b><u>∠A = 130°</b></u>$