The sum of the unknown angles is equal to m∠XYZ.
m∠XYW=32^(∘) and m∠WYZ=85^(∘)
Practice makes perfect
The expression m∠XYW indicates the measure of the angle between two rays, YX and YW. Similarly, the expression m∠WYZ indicates the measure of the angle between rays YW and YZ. 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∠XYZ is equal to the sum of m∠WYZ and m∠XYZ. We can solve for x by creating an equation using the expressions for the two smaller angles and the value of the larger angle.
Having solved the equation, we can calculate the individual angles by substituting x= - 2 into the expressions for the unknown angles.
m∠XYW:& 6( - 2)+44=32^(∘)
m∠WYZ:& - 10( - 2)+65 =85^(∘)
