Question

The quadrilateral RSTU is inscribed in the circle shown below. S R U Jake wants to prove the theorem that says that the measure of the quadrilateral's opposite angles add to 180°. He knows that the measure of angle Ris half the measure of are STU and that the measure of angle T is half the measure of arc SRU. Which of the following is an appropriate step to prove that ZR + ZT =180°?

Answer 1

Arc STU and arc SRU can form the complete circle. Therefore

`Therefore,[tex]\begin{gathered} 2R+2T=360^0 \\ \text{factorize left hand side} \\ 2(R+T)=360^0 \end{gathered}`

Dividing both sides by 2, we have

[tex]Hence, the appropriate steps are: Assume that the measure of arcs STU and SRU add up to 360 degrees

Also, substitute 2 m

pick yes in options 2 and 3

pick no in options 1 and 4