Exercise 4 Page 304

We want to find the measure of ∠ 4 and ∠ 5. First, let's notice that ∠ 4 and ∠ 5 form a linear pair.

Now let's recall that if two angles form a linear pair then they are supplementary angles according to the Supplement Theorem. This means that ∠ 4 and ∠ 5 are supplementary angles and the sum of their measures is 180. m∠ 4+m∠ 5 = 180 Now, we are given that m∠ 4= 3(x-1) and m∠ 5= x+7. Let's use this information and substitute the given expressions into the equation. Then we will be able to solve for x.

m∠ 4+m∠ 5 = 180

SubstituteII

m∠ 4= 3(x-1), m∠ 5= x+7

3(x-1) + x+7 = 180

▼

Solve for x

Distr

Distribute 3

3x-3+x+7=180

AddSubTerms

Add and subtract terms

4x+4=180

SubEqn

LHS-4=RHS-4

4x=176

DivEqn

.LHS /4.=.RHS /4.

x=44

The value of x is 44. Finally, we can find the measures of ∠ 4 and ∠ 5 by substituting 44 for x into their expressions. Let's start with m∠ 4.

m∠ 4=3(x-1)

Substitute

x= 44

m∠ 4=3( 44-1)

SubTerm

Subtract term

m∠ 4 = 3(43)

Multiply

Multiply

m∠ 4 = 129

The measure of ∠ 4 is 129. Now we can find the measure of ∠ 5 in the similar way. Let's do it!

m∠ 5=x+7

Substitute

x= 44

m∠ 5= 44+7

AddTerms

Add terms

m∠ 5=51

The measure of ∠ 5 is 51. Therefore, thanks to the Supplement Theorem, we were able to find the measures of the numbered angles.