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

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

Answer 2

`\boxed{\boxed{x^(\circ)=78^(\circ)}}`

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)`