The sum of the unknown angles is equal to m∠RST.
m∠RSQ=32^(∘)
m∠TSQ=58^(∘)
Practice makes perfect
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^(∘)
