Answer:
x = 90 degrees
Explanation:
the above figure is of a circle, so the sum of the measures of angles will be 360 degrees.
measure of arc = measure of the angle inscribed by the arc
therefore, the measure of arc JK will also be x...... ( vertically opposite angles)
therefore, x + x + 30 + (2x - 30) = 360 .....(1)
therefore, 2x + 30 + 2x - 30 = 360
therefore, 4x = 360.....( as -30 and +30 will be cancelled)
therefore, x = 90 degrees
Cross correction:-
by putting in x = 90 in (1)
90 + 90 + 30 + 2*90 - 30 = 360
180 + 30 + 180 - 30 = 360
180 + 180 = 360
so, x= 90 degrees is verified.