Question

Item 6 sq−→sq→ bisects ∠rst∠rst, sp−→sp→ bisects ∠rsq∠rsq, and sv−→sv→ bisects ∠rsp∠rsp. the measure of ∠vsp∠vsp is 17°17°. find m∠tsqm∠tsq.

Answer 1

Angle TSQ measures 68 degrees. When a ray bisects an angle, it divides it into two equal parts. Each part is one-half the measurement of the original angle. Several rays are described as bisecting different angles. I would sketch a diagram to keep track of all the different rays and angles.
       
A. Since angle RST is bisected by ray SQ, angle RSQ and angle QST are each half the size of angle RST.
       
B. Since angle RSQ is bisected by ray SP, angle RSP and angle PSQ are each half the size of angle RSQ.
       
C. Since angle RSP is bisected by ray SV, angle RSV and angle VSP are each half the size of angle RSP. We are given the measurement of angle VSP as 17 degrees. To find the measure of angle RSP, we notice in statement C above that VSP is half the size of angle RSP. If we double angle VSP's measurement (multiply by 2), we get angle RSP measures 34 degrees. Using similar logic and statement B above, we double RSP's measurement of 34 to get angle RSQ's measurement. Double 34 is 68, angle RSQ's measurement in degrees. From statement A above, we notice that RSQ's measurement is equal to that of angle QST's. Therefore, angle QST also measures 68 degrees. However, the question asks us to find the measurement of angle TSQ. However, angle QST and angle TSQ are the same. Either description can be used. Therefore, the measurement of angle TSQ is 68 degrees.