prove that angles in a semi circle are equal to 90 degree

consider a circle with diameter AB subtending an angle APB in the segment i.e the semicircle. now, angle AOB = 180 degree.

also, angle APB = 1/2 of angle AOB (the angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle)

angle APB = 1/2 * 180 degree.

angle APB = 90 degree...

therefore the angle in a semicircle is 90 degree..

hope it helped :)