Exercise 20 Page 116

We know that the ratio of the interior angles measures of a triangle is 2: 3: 5. In this case, this means that for every 2 degrees of the first angle, there are 3 degrees of the second angle, and 5 degrees of the third angle. As a result, the measures of the interior angles are 2x^(∘), 3x^(∘), and 5x^(∘). Let's draw the triangle!

Notice that all of the interior angle measures are represented by a variable x multiplied by a number. We can write an equation that relates all of the interior angle measures. To do so, we will use the rule for the interior angle measures of a triangle.

Interior Angle Measures of a Triangle

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

By this rule, the following relation is true. 2x^(∘)+ 3x^(∘)+ 5x^(∘) = 180^(∘) Let's solve the equation for x!

2 x + 3 x + 5 x = 180

AddTerms

Add terms

10 x = 180

DivEqn

.LHS /10.=.RHS /10.

x = 18

We found that x= 18. We can substitute 18 for x to find the measures of interior angles of the triangle.

Interior Angle Measures
2x^(∘)	2( 18)^(∘)	36^(∘)
3x^(∘)	3( 18)^(∘)	54^(∘)
5x^(∘)	5( 18)^(∘)	90^(∘)

The measures of the interior angles of the triangle are 36^(∘), 54^(∘), and 90^(∘).