The expression m∠ RSQ indicates the measure of the angle between two rays, SR and SQ. Similarly, the expression m∠ TSQ indicates the measure of the angle between rays ST and SQ. To find their measures, let's start by identifying the three angles on a diagram.
Looking at the figures, and by the Angle Addition Postulate, we can see that m∠ RST is equal to the sum of m∠ RSQ and m∠ TSQ. We can solve for x by creating an equation using the expressions for the two smaller angles and the value of the larger angle. Note that ∠ RST is a right angle which is always equal to 90^(∘).
Having solved the equation, we can calculate the individual angles by substituting x= 5 into the expressions for the unknown angles.
m∠ RSQ:& 15( 5)-43=32^(∘)
m∠ TSQ:& 8 ( 5)+18 =58^(∘)
