Exercise 31 Page 429

We are given two angles, ∠ U and ∠ V. We want the angles to be complements of each other. This means that we want the sum of their measures to be 90. m∠ U + m∠ V = 90^(∘)We are told that the measure of ∠ U is 2x^(∘), and that the measure of ∠ V is four times the measure of ∠ U. lm∠ U =2x^(∘) m∠ V=4m∠ U ⇒ m∠ V=8x^(∘) Finally, we will substitute m∠ U = 2x and m∠ V = 8x in the first equation we wrote.

m∠ U + m∠ V = 90^(∘)

SubstituteII

m∠ U= 2x, m∠ V= 8x

2x + 8x = 90

AddTerms

Add terms

10x=90

DivEqn

.LHS /10.=.RHS /10.

x=9

With x=9 the angles are complements of each other. Therefore the correct answer is B.