body{margin:0;} noscript{z-index: 10000; position: fixed; display: block; height: 100%; width: 100%; background: #fff;} noscript .fa{font-size: 40px; display:block; color: #daa520;} noscript div{margin-top: 6%; padding-left: 20px; padding-right: 20px; text-align: center;} ! You must have JavaScript enabled to use this site.

Core Connections Integrated II, 2015

CC

Core Connections Integrated II, 2015 View details

3. Section 8.3

Continue to next subchapter

Exercise 73 Page 456

Practice makes perfect

a To determine the sum of the interior angles of an n-gon, we can use the following formula.

180^(∘)(n-2) By substituting n=5 into the formula we determine the sum of the interior angles.

180^(∘)(n-2)

n= 5

180^(∘)( 5-2)

Subtract term

180^(∘)(3)

Multiply

540^(∘)

When we know the sum of the interior angles we can write an equation that contains x. x+x+125^(∘)+125^(∘)+90^(∘)=540^(∘) Let's solve this equation.

x+x+125^(∘)+125^(∘)+90^(∘)=540^(∘)

Add terms

2x+340^(∘)=540^(∘)

LHS-340^(∘)=RHS-340^(∘)

2x=200^(∘)

.LHS /2.=.RHS /2.

x=100^(∘)

b The given angles are alternate exterior angles.

Because the two lines cut by the third line are parallel, we can by the Alternate Exterior Angles Theorem claim that these are congruent. With this information, we can write the following equation. 6x+18^(∘)=2x+30^(∘) Let's solve this equation.

6x+18^(∘)=2x+30^(∘)

LHS-18^(∘)=RHS-18^(∘)

6x=2x+12^(∘)

LHS-2x=RHS-2x

4x=12^(∘)

.LHS /4.=.RHS /4.

x=3^(∘)

Subchapter links

8.3.1 Area Ratios of Similar Figures p.451-452

8.3.2 Ratios of Similarity p.455-457