Exercise 2 Page 745

An angle whose vertex is on a circle and whose sides are chords of the circle is an inscribed angle. Therefore, in the given diagram, ∠ S is an inscribed angle and it measures 63^(∘). We want to know the measure of RT, that is the intercepted arc of this angle.

According to the Inscribed Angle Theorem, the measure of an inscribed angle is half the measure of its intercepted arc. This means that m ∠ S is half the measure of RT.

m ∠ S=m RT/2

Substitute

m ∠ S= 63

63=m RT/2

MultEqn

LHS * 2=RHS* 2

126=m RT

RearrangeEqn

Rearrange equation

m RT=126

We found that mRT= 126.