Question

Assume that lines that appear to be tangent are tangent. O is the center of the circle. Find the value of x. (Figures are not drawn to scale.)

(Figure and terms in pictures)

A. 315
B. 67.5
C. 45
D. 270

Answer 1

The correct answer is c

Answer 2

The value of x is 45°

Option C is correct.

Explanation:

Given the figure in which two tangents are drawn and

The measure of ∠O is 135°

we have to find the value of x.

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

∠OAB=∠OCB=90°

As OABC is a quadrilateral therefore sum of all angles equals to 360°

∠ABC+∠AOC+∠OAB+∠OCB=360°

x°+135°+90°+90°=360°

x+315°=360°

x=360°-315°=45°

Hence, the value of x is 45°

Option C is correct.