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.
Attached Figure / Diagram
A
130°
B
115°
C
58°
D
68°
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
Alternate segments are equal : R^\circ = 64^\circ
An isosceles triangle has two angles ( Q^\circ & N^\circ ) equal as A^\circ
R^\circ + A^\circ + A^\circ = 180^\circ
2A^\circ= 180 - 64
2A^\circ = 116^\circ
A = \(\frac{116}{2}\)
A = 58.
: Q^\circ = 58, N^\circ = 58 and T^\circ = 58
As Alternate segments are equal: T = Q
Source: WAEC / JAMB / NECO Classroom Archive (Record #61423)