Exercise 13 Page 132

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. Recall that the measure of a right angle is 90^(∘). x^(∘)+ (x+8)^(∘)+ 90^(∘)=180^(∘) Let's solve the equation and find the value of x. For simplicity, we will not write the degree symbol.

x+(x+8)+90=180

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Solve for x

RemovePar

Remove parentheses

x+x+8+90=180

AddTerms

Add terms

2x+98=180

SubEqn

LHS-98=RHS-98

2x=82

DivEqn

.LHS /2.=.RHS /2.

x=41

The measure of the angle is 41^(∘). To find the other missing measure, we will substitute x= 41 in the expression for the remaining angle, (x+8)^(∘). Once again, we will remove the degree symbol for the calculation.

x+8

Substitute

x= 41

41+8

AddTerms

Add terms

49

The measure of the third angle is 49^(∘). This means that the measures of the interior angles of the triangle are 41^(∘), 49^(∘), and 90^(∘).