Question

Point O is the center of the circle. what is the value of x?

Answer 1

Answer:

Measure of angle x is 34°

Step-by-step explanation:

Given the figure where O is the center of the circle

we have to find the value of x.

∠ORQ=62°   (Given)

By theorem radius from the center of circle is perpendicular to the tangent line.

∴∠OQP=90°

As OR=OQ both are the radii of same circle ∴ ∠ORQ=∠OQR

In ΔOQR by angle sum property of triangle

∠ORQ+∠OQR+∠QOR=180°

62°+62°+∠QOR=180°

∠QOR=56°

In ΔOQP by angle sum property of triangle

∠OPQ+∠OQP+∠QOP=180°

x+90°+56°=180°

x=34°

Hence, measure of angle x is 34°

Answer 2

180 - 2·62 = 56

180 - 56 - 90 = 34°