Assume that lines that appear to be tangent are tangent. Point O is the center of the circle. Find the value of x if the m < P = 28

A) 64
B) 62
C) 68
D) 66

1 answer

Since angle P is equal to the central angle of arc PR, and angle P is 28 degrees, then the measure of arc PR is also 28 degrees.

Since angle Q and angle R are angles formed by a tangent and a chord, they are supplementary. Therefore, angle Q = 180 - angle R.

The measure of arc PR is equal to the measure of angle QR (angle formed by a chord and an inscribed angle). Therefore, angle QR = 28 degrees.

Since angle Q and angle R are supplementary, we have:

180 - angle R = 28
angle R = 180 - 28
angle R = 152

Since angle R and angle S are angles formed by a tangent and a chord, they are supplementary. Therefore, angle R + angle S = 180.

152 + angle S = 180
angle S = 180 - 152
angle S = 28

Since angle S and angle O are angles formed by a tangent and a chord, they are equal in measure:

angle S = angle O
28 = x

Therefore, x = 28.

So, the value of x is 28.

Correct answer: x) 28