Exercise 2 Page 112

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-35)^(∘)+ 43^(∘)=180^(∘) Let's solve the equation and find the value of x. For simplicity, we will not write the degree symbol.

x+(x-35)+43=180

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Solve for x

RemovePar

Remove parentheses

x+x-35+43=180

AddTerms

Add terms

2x+8=180

SubEqn

LHS-8=RHS-8

2x=172

DivEqn

.LHS /2.=.RHS /2.

x=86

The measure of one of the angles is 86^(∘). To find the other missing measure, we will substitute x= 86 in the expression for the remaining angle, (x-35)^(∘). Once again, we will remove the degree symbol for the calculation.

x-35

Substitute

x= 86

86-35

AddTerms

Add terms

51

The measure of the third angle is 51^(∘).