Exercise 13 Page 115

We want to find the measures of the angles in the given triangle.

To find these angle measures, we will first recall a key piece of information!

Angle Sum of a Triangle

The sum of the measures of the interior angles of a triangle is 180^(∘).

With this rule, we can write an equation connecting the measures of the angles of our triangle. x^(∘)+ (x-44)^(∘)+ 48^(∘)=180^(∘) Let's solve the equation and find the value of x. For simplicity, we will not write the degree symbol.

x+(x-44)+48=180

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Solve for x

RemovePar

Remove parentheses

x+x-44+48=180

AddTerms

Add terms

2x+4=180

SubEqn

LHS-4=RHS-4

2x=176

DivEqn

.LHS /2.=.RHS /2.

x=88

The measure of one of the angles is 88^(∘). To find the other missing measure, we will substitute x= 88 in the expression for the remaining angle, (x-44)^(∘). Once again, we will remove the degree symbol for the calculation.

x-44

Substitute

x= 88

88-44

AddTerms

Add terms

44

The measure of the third angle is 44^(∘).