Sketch a visual step by step to represent the scenario.
68^(∘)
Practice makes perfect
First we are going to repeat the steps in the exercise. Therefore, we begin by drawing two rays which we call SR and ST.
Next we draw a ray SQ which bisects the ∠ RST.
Since we bisected ∠ RST, we know that m∠ TSQ=m∠ RSQ. We are now going to draw SP which bisects ∠ RSQ.
The ray SP bisects ∠ RQ and we know that m∠ RSP=m∠ PSQ. Let's now create the ray SV which bisects ∠ RSP. Let's also mark that we know that the m∠ VSP=17^(∘).
The ray SV bisects ∠ RSP. Consequently m∠ RSP is twice as large as the m∠ VSP. Therefore we know the following.
m∠ RSP=2* m∠ VSP=2* 17^(∘) = 34 ^(∘)
Let's mark this in the diagram.
The ray SP bisects ∠ RSQ. Therefore m∠ RSQ is twice as large as the m∠ RSP.
m∠ RSQ=2* m∠ RSP=2* 34^(∘) = 68 ^(∘)
Let's remove the ray SP and mark the m∠ RSQ in the diagram.
We remember that the ray SQ bisects the ∠ RST. The resulting angles after the bisection, ∠ TSQ and ∠ RSQ, have the same size and therefore have the same measure.
