Answer:
Measure of angle x is 34°
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°