Exercise 14 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-11)^(∘)+ 73^(∘)=180^(∘) Let's solve the equation and find the value of x. For simplicity, we will not write the degree symbol.

x+(x-11)+73=180

▼

Solve for x

RemovePar

Remove parentheses

x+x-11+73=180

AddTerms

Add terms

2x+62=180

SubEqn

LHS-62=RHS-62

2x=118

DivEqn

.LHS /2.=.RHS /2.

x=59

The measure of one of the angles is 59^(∘). To find the other missing measure, we will substitute x= 59 in the expression for the remaining angle, (x-11)^(∘). Once again, we will remove the degree symbol for the calculation.

x-11

Substitute

x= 59

59-11

SubTerms

Subtract terms

48

The measure of the third angle is 48^(∘).