Question

Complete the following proof. Given: SW is diameter of circle R m ST = 30° Prove: m RTW = 15°

Answer 1

Answer:

see the explanation

Step-by-step explanation:

The picture of the question in the attached figure

we know that

1) $arc\ ST=30^o$ ----> is given

2) $m\ angle SRT=30^o$ ----> by central angle

3) $m\angle RWT=\frac{1}{2}[arc\ ST]$ ----> by inscribed angle

$m\angle RWT=\frac{1}{2}[30^o]=15^o$

4) $m\angle RTW=m\angle RWT$ ----> Triangle RTW is an isosceles triangle (RT=RW=radius of circle R)

therefore

$m\angle RTW=15^o$