Question

How do i find x? pls tell me with working

Answer 1

Answer:

35

Step-by-step explanation:

Angle QRS is an inscribed angle, so measure of angle QRS is half the measure of the intercepted arc, arc SPQ. Therefore arc SPQ is 125*2 = 250 degrees, and arc QRS is 360 - 250 = 110 degrees.

Angle QPS is an inscribed angle, and arc QRS is its intercepted arc. Therefore angle QPS is 110/2 = 55 degrees. Since PS is the radius of the circle, angle PQS, the angle inscribed in the semicircle, is 90 degrees. Since interior angles of the triangle QPS add up to 180 degrees, angle QSP is 180 - 90 - 55 = 35 degrees.

Angles QSP and UST are vertical angles, and by the vertical angles theorem, they are congruent. Therefore x = 35.