Answer:
Step-by-step explanation:
Note that ∠TSU and ∠PSR are vertical angles. Hence:
∠PSR is the sum of ∠PSQ and ∠QSR. Hence:
We know that ∠TSU measures 4<em>x</em> and ∠QSR measures 3<em>x</em>. Thus:
Solve for ∠PSQ:
Next, ∠PQS and ∠RQS form a linear pair. Thus:
∠RQS measures 68°. Thus:
Solve for ∠PQS:
The interior angles of a triangle must total 180°. So, for ΔPQS:
Substitute in the known values:
Simplify:
And divide. Hence:
