Exercise 12 Page 115

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

25^(∘), 45^(∘), and 110^(∘)

Practice makes perfect

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+65)^(∘)+ 25^(∘)=180^(∘) Let's solve the equation and find the value of x. For simplicity, we will not write the degree symbol.

x+(x+65)+25=180

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Solve for x

RemovePar

Remove parentheses

x+x+65+25=180

AddTerms

Add terms

2x+90=180

SubEqn

LHS-90=RHS-90

2x=90

DivEqn

.LHS /2.=.RHS /2.

x=45

The measure of one of the angles is 45^(∘). To find the other missing measure, we will substitute x= 45 in the expression for the remaining angle, (x+65)^(∘). Once again, we will remove the degree symbol for the calculation.

x+65

Substitute

x= 45

45+65

AddTerms

Add terms

110

The measure of the third angle is 110^(∘).