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Sum of Pair of Opposite Angles in Quadrilateral

In the given ...

Question

In the given figure $□ M N O P$ is a cyclic quadrilateral. If $∠ P = 5 x + 12$ , and $∠ N = 3 x + 8$ then find the value of $x$ and also the measures of $∠ P$ and $∠ N$ .

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Solution

In a cyclic quadrilateral ,oppostie angles are supplimentary,
$∠ P + ∠ N = 180 5 x + 12 + 3 x + 8 = 180 8 x + 20 = 180 8 x = 160 x = 20 ∠ P = 5 (20) + 12 = 112 ∠ N = 3 (20) + 8 = 68$

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