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Quadrilateral ABCD is inscribed in a circle such that:

Quadrilateral ABCD is inscribed in a circle such that:-example-1
User Jaxxbo
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1 Answer

2 votes

Answer:

∠ C = 84°

Explanation:

A quadrilateral inscribed in a circle is a cyclic quadrilateral.

the opposite angles sum to 180° , that is

∠ A + ∠ C = 180 , then

x² + 60 + 8x + 36 = 180

x² + 8x + 96 = 180 ( subtract 180 from both sides )

x² + 8x - 84 = 0 ← in standard form

(x + 14)(x - 6) = 0 ← in factored form

equate each factor to zero and solve for x

x + 14 = 0 ⇒ x = - 14

x - 6 = 0 ⇒ x = 6

x > 0 , then x = 6 , so

∠ C = 8x + 36 = 8(6) + 36 = 48 + 36 = 84°

User Brune
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