Question

Find the measures of the angles in the diagram. 20 points for all of the ones listed below

AQB

ASB

ALB

ATB

ARB

BWD

Answer 1

all are 90 degrees, except for bwd

Answer 2

AB is a diameter of the circle, so it divides circle into two semicircles.

Inscribed Angle Theorem:

The measure of an inscribed angle is half the measure of the intercepted arc.

An especially interesting result of the Inscribed Angle Theorem is that an angle inscribed in a semi-circle is a right angle. That's why m∠AQB=m∠ASB=m∠ALB=m∠ATB=m∠ARB=90°.

It is impossible to find measure of ∠BWD, its measure depends on measure of a central angle ∠WDB.