Question

If the m RQT = 155 degrees, determine m RQS.

Answer 1

The angle ∠RQT is the sum of the angles ∠RQS and ∠SQT, since they are adjacent.

So we have that:

$\begin{gathered} \angle\text{RQS}+\angle\text{SQT}=\angle\text{RQT} \\ 4x-20+3x+14=155 \\ 7x=155+20-14 \\ 7x=161 \\ x=23 \end{gathered}$

Now, calculating the angle ∠RQS, we have:

$\begin{gathered} \angle\text{RQS}=4x-20 \\ \angle\text{RQS}=4\cdot23-20 \\ \angle\text{RQS}=92-20 \\ \angle\text{RQS}=72\degree \end{gathered}$

So the angle ∠RQS measures 72°.