Answer:
(A) [tex]x=61^{\circ}[/tex]
Step-by-step explanation:
Given: O is the center of the circle and ∠OPQ=29°.
To find: The value of x.
Solution:
We know that A tangent to a circle forms a right angle with the circle's radius, at the point of contact of the tangent, therefore ∠OQP=90°.
Now, using the angle sum property in ΔOPQ, we ahve
[tex]{\angle}OPQ+{\angle}PQO+{\angle}QOP=180^{\circ}[/tex]
Substituting the given values, we get
⇒[tex]29^{\circ}+90^{\circ}+x=180^{\circ}[/tex]
⇒[tex]119^{\circ}+x=180^{\circ}[/tex]
⇒[tex]x=61^{\circ}[/tex]
Hence, the value of x is 61 degrees.
Thus, option A is correct.
