Exercise 13 Page 52

We have been given a pair of complementary angles and their measures written as algebraic expressions. m∠ UVW=& (x-10)^(∘) m∠ XYZ=& (4x-10)^(∘)Since the angles are complementary, we know that the sum of their measures should equal 90^(∘). We can solve for x by creating an equation using the expressions for the two smaller angles and their sum.

m∠ UVW + m∠ XYZ = 90

SubstituteII

m∠ UVW= x-10, m∠ XYZ= 4x-10

( x-10) + ( 4x-10) = 90

RemovePar

Remove parentheses

x-10 + 4x-10 = 90

AddSubTerms

Add and subtract terms

5x-20 = 90

AddEqn

LHS+20=RHS+20

5x = 110

DivEqn

.LHS /5.=.RHS /5.

x=22

Now we can substitute this value of x into the given expressions to find the measures of the angles. m∠ UVW ⇒ & 22-10=12^(∘) m∠ XYZ ⇒ & 4( 22)-10=78^(∘)