In the diagram, TS is a tangent to the circle at S. |PR| and < PQR = 177o. Calculate < PST.
Attached Figure / Diagram
A
54o
B
44o
C
34o
D
27o
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
In the diagram above, x1 = 180o - 117o = 63o(opposite angles of a cyclic quad.)
x1 = x2 (base angles of isos. \(\Delta\))
x\(_1\) + x\(_2\) + \(\alpha\) = 180º (sum of angles of a \(\Delta\)
63º + 63º + \(\alpha\) = 180º
\(\alpha\) = 180º - (63 + 63)º
= 54º
< PST = 54º (aalternate angles)
Source: Myschool Past Questions Archive (Record #46173)