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Big Ideas Math Algebra 1, 2015

BI

Big Ideas Math Algebra 1, 2015 View details

Chapter Review

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Exercise 10 Page 44

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

Value of x: 10
Measures of Angles: 110^(∘), 50^(∘), 20^(∘)

Practice makes perfect

We are given that the sum of the interior angles of the given triangle is 180^(∘). Let's take a look at the given figure!

triangle

We can write an equation that adds all of the angles together and is equal to 180^(∘). 110^(∘)+5x^(∘)+2x^(∘)=180^(∘) By solving this equation for x, we will be able to find the measure of the two missing angles.

110+5x+2x=180

Add terms

110+7x=180

LHS-110=RHS-110

110+7x-110=180-110

Subtract terms

7x=70

.LHS /7.=.RHS /7.

7x/7=70/7

MovePartNumRight

a* b/c=a/c* b

7/7x=70/7

Calculate quotient

x=10

We know now that the value of x is 10 and we also know the value of one of the angles, 110^(∘). To find the value of the two missing angles, we substitute 10 for x in 5x and in 2x. 5x^(∘) ⇒ 5* 10^(∘)= 50^(∘) 2x^(∘) ⇒ 2* 10^(∘)= 20^(∘) Therefore, the two missing angles are 50^(∘) and 20^(∘).

Subchapter links

Exercises p.44-46