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:

$\boxed{\boxed{x^{\circ}=78^{\circ}}}$

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,

$\Rightarrow m\angle O+m\angle Q+m\angle P=180^{\circ}$

$\Rightarrow x^{\circ}+90^{\circ}+12^{\circ}=180^{\circ}$

$\Rightarrow x^{\circ}=180^{\circ}-90^{\circ}-12^{\circ}=78^{\circ}$

Answer 2

Angle q is right angle so you would first do 12+90=102 then you would do 180-102=78 so x=78