Mathematics
In cyclic quadrilateral ABCD, ∠A = 3∠C and ∠D = 5∠B. Find the measure of each angle of the quadrilateral.
Circles
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Answer
Given, cyclic quadrilateral ABCD
So, ∠A + ∠C = 180° [Opposite angles in a cyclic quadrilateral is supplementary]
⇒ 3∠C + ∠C = 180° [As ∠A = 3∠C]
⇒ 4∠C = 180°
⇒ ∠C =
⇒ ∠C = 45°.
Now,
⇒ ∠A = 3∠C = 3 x 45° = 135°.
Similarly,
⇒ ∠B + ∠D = 180°
⇒ ∠B + 5∠B = 180° [As, ∠D = 5∠B]
⇒ 6∠B = 180°
⇒ ∠B =
⇒ ∠B = 30°.
Now,
⇒ ∠D = 5∠B = 5 x 30° = 150°.
Hence, ∠A = 135°, ∠B = 30°, ∠C = 45° and ∠D = 150°.
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