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.

  • A 130°
  • B 115°
  • C 58°
  • D 68°
waec 2021mathematics

The correct answer is C. 58°

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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