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.

McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

4. Proving Angle Relationships

Continue to next subchapter

Exercise 3 Page 304

Do the angles form a linear pair? If so, what can you get from this?

Measures: m∠ 4 = 114 and m∠ 5 = 66
Theorem: Supplement Theorem

Practice makes perfect

Notice that ∠ 4 and ∠ 5 form a linear pair.

The Supplement Theorem tells us that they are supplementary angles, and we get the following relation. m∠ 4+m∠ 5 = 180 Now, let's substitute m∠ 4= 2x and m∠ 5= x+9 into this equation and solve for x.

m∠ 4+m∠ 5 = 180

m∠ 4= 2x, m∠ 5= x+9

2x + x+9 = 180

▼

Solve for x

Add terms

3x+9=180

LHS-9=RHS-9

3x=171

.LHS /3.=.RHS /3.

x=57

Finally, we find the measures of ∠ 4 and ∠ 5 by substituting x= 57 into their expressions. lll m∠ 4=2x & ⇒ & m∠ 4=2( 57) & & =114 m∠ 5=x+9 & ⇒ & m∠ 5= 57+9 & & =66

Subchapter links

Exercises p.304-307