Answer:
The value of the angle x is 30°
Explanation:
We know that the line OQ is tangent to the line QP, which means that the angle between these lines is 90°.
On the other hand, the lines OQ and OB (look at the attachment) have the same length and both have the length of the circle's ratio.
This brings us to the conclusion that the triangle formed by points O, Q and B is equilateral, so all the sides and angles are equal.
As we know the angles BOQ is 60°, for what the angle POQ has 60° too.
It is ruled that the sum of all the angles on a triangle is 180°. so we have the following equation:
angle PQO + angle QOP + angle OPQ = 180°
90°+60°+ X°=180°
If we isolate X, we get:
X°= 180° - 90° - 60°
X°= 30°
the angle OPQ or X is 30°.