Answer:
[tex]\boxed{\boxed{x^{\circ}=78^{\circ}}}[/tex]
Step-by-step explanation:
Given that, O is the center of the circle and PQ is a tangent to the circle at point Q. OQ is a radius of the circle.
We know that, a tangent to a circle is a line which just touches the circle. And the angle between the tangent and radius is 90°.
Hence, ΔOQP is a right angle triangle. We know that the sum of the measurements of all the 3 angles of a triangle leads to 180°. So,
[tex]\Rightarrow m\angle O+m\angle Q+m\angle P=180^{\circ}[/tex]
[tex]\Rightarrow x^{\circ}+90^{\circ}+12^{\circ}=180^{\circ}[/tex]
[tex]\Rightarrow x^{\circ}=180^{\circ}-90^{\circ}-12^{\circ}=78^{\circ}[/tex]
