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ICSE-VIII-Mathematics

16: Understanding Shapes (Including Polygons) Class 8 Maths

with Solutions - page 8
Qstn# C-7 Prvs-QstnNext-Qstn
  • #7
    Given : In quadrilateral ABCD ; ∠C = 64°, ∠D = ∠C - 8° ; ∠A = 5(a + 2)° and ∠B = 2(2a + 7)°.
    Calculate ∠A.
    Ans : ∠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°