Question

O is the center of the circle. Assume that lines that appear to be tangent are tangent. What is the value of x?

Answer 1

Answer:

(A) $x=61^{\circ}$

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

${\angle}OPQ+{\angle}PQO+{\angle}QOP=180^{\circ}$

Substituting the given values, we get

⇒$29^{\circ}+90^{\circ}+x=180^{\circ}$

⇒$119^{\circ}+x=180^{\circ}$

⇒$x=61^{\circ}$

Hence, the value of x is 61 degrees.

Thus, option A is correct.

Answer 2

Hello : 
29° +90°+X° =  180° 
x° = 180°-90°-29°
x° = 61°...(first answer)