In the figures, PQ is a tangent to the circle at R and UT is parallel to PQ. if < TRQ = xo, find < URT in terms of x
Attached Figure / Diagram
A
2xo
B
(90 - x)o
C
(90 + x)o
D
(180 - 2x)o
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
< URT = < TRQ (angle alternate a tangent and a chord equal to angle in the alternate segment)
< RUT = xo
In \(\bigtriangleup\) URT
< RUT + < RUT + < UTR = 180o (sum of int. < s of \(\bigtriangleup\))
< URT + x + x = 180o
< URT = 180o - 2x
Source: WAEC / JAMB / NECO Classroom Archive (Record #37009)