question_answer

  If TA is a tangent to the circle at B, what is the value of x + y + z?

A) \[56{}^\circ \]

B) \[112{}^\circ \]

C) \[28{}^\circ \]

D) \[65{}^\circ \]

Correct Answer: A

Solution :

[a] \[X=\angle PQB=28{}^\circ \] (angles in alternate segment) also, \[OB\bot TB\] we get, \[\angle POB=90{}^\circ -x=90{}^\circ -28{}^\circ \] \[=62{}^\circ \] Now, in BPQ \[\angle BPQ+\angle PBQ+\angle PQB=180{}^\circ \] \[(62+y)+(62+z)+x=180\] \[x+y+z=180-2\times 62\] \[=180-124=56{}^\circ \]