$In the diagram, $\overline{MP}$ is a tangent to the circle NQR, ∠NQR, ∠PNQ = 64 and | $\overline{RQ}$ | = | $\overline{RN}$ |. Find the angle market t.$

In the diagram, $\overline{MP}$ is a tangent to the circle NQR, ∠NQR, ∠PNQ = 64 and | $\overline{RQ}$ | = | $\overline{RN}$ |. Find the angle market t.

130°

115°

58°

68°

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Correct answer is C

Alternate segments are equal : R° = 64°

An isosceles triangle has two angles ( Q° & N° ) equal as A°

R° + A° + A° = 180°

2A°= 180 - 64

2A° = 116°

A = $\frac{116}{2}$

A = 58.

: Q° = 58, N° = 58 and T° = 58

As Alternate segments are equal: T = Q

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In the diagram, $\overline{MP}$ is a tangent to the circle NQR, ∠NQR, ∠PNQ = 64 and | $\overline{RQ}$ | = | $\overline{RN}$ |. Find the angle market t.

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In the diagram, $\overline{MP}$ is a tangent to the circle NQR, ∠NQR, ∠PNQ = 64 and | $\overline{RQ}$ | = | $\overline{RN}$ |. Find the angle market t.