The angle at the circumference in a semi-circle is 90°. Angle STU = 90° Angles in a triangle add up to 180°. The angle on a straight line is 180°. The angle VOY = 180°. The angle at the ...

More simply, angles in the same segment are equal. Let the obtuse angle MOQ = \(2x\). Using the circle theorem, the angle at the centre is twice the angle at the circumference. Angle MNQ = \(x ...