Find the value of the angle marked x in the diagram above

Explanation

\(PR^2 = PQ^2 + RQ^2 - 2(PQ)(RQ)cos Q\)

\(\implies cos Q = \frac{PQ^2 + RQ^2 - PR^2}{2(PQ)(RQ)}\)

\(\implies cos Q = \frac{8^2 + 5^2 - 7^2}{2\times8\times5}\)

\(\implies cos Q = \frac{64 + 25 - 49}{80}\)

\(\implies cos Q = \frac{40}{80} = 0.5\)

\(\implies Q = cos^{-1} (0.5) = 60^0\)

\(\therefore x = 60^0\)

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