DashboardNewsSettingsHelp
Get Premium
Dashboard
Dashboard Sign out
McGraw Hill Integrated II, 2012
MH
McGraw Hill Integrated II, 2012 View details
4. Proving Angle Relationships
Continue to next subchapter
search

Exercise 12 Page 305

Are ∠ 3 and ∠ 4 vertical angles? If so, what can you get from this?

Measures: m∠ 3=m∠ 4=113
Theorem: Vertical Angles Theorem.

Practice makes perfect

We are given the following system of equations. m∠ 3=2x+23 & (I) m∠ 4=5x-112 & (II) But also, from the diagram below we can see that ∠ 3 and ∠ 4 are vertical angles.

Hence, using the Vertical Angles Theorem, we obtain that ∠ 3 ≅ ∠ 4 and then, m∠ 3=m∠ 4. Using this fact, we can equate the equations in the given system and solve it for x.

m∠ 3=2x+23 & (I) m∠ 4=5x-112 & (II)
Substitute

(I): m∠ 3= m∠ 4

m∠ 4=2x+23 m∠ 4=5x-112
â–¼
(II): Solve by substitution
Substitute

(II): m∠ 4= 2x+23

m∠ 4=2x+23 2x+23=5x-112
SubEqn

(II): LHS-2x=RHS-2x

m∠ 4=2x+23 23=3x-112
AddEqn

(II): LHS+112=RHS+112

m∠ 4=2x+23 135=3x
RearrangeEqn

(II): Rearrange equation

m∠ 4=2x+23 3x=135
DivEqn

(II): .LHS /3.=.RHS /3.

m∠ 4=2x+23 x=45

Now that we found the value of x, let's substitute it into the first equation to find m∠ 4.

m∠ 4=2x+23 x=45
Substitute

(I): x= 45

m∠ 4=2( 45)+23 x=45
Multiply

(I): Multiply

m∠ 4=90+23 x=45
AddTerms

(I): Add terms

m∠ 4=113 x=45

Finally, remember that ∠ 3≅ ∠ 4, which implies that m∠ 3=113 as well.

Subchapter links expand_more
arrow_right Exercises p.304-307
1
Exercises 2 (Page 304)
Exercises 3 (Page 304)
Exercises 4 (Page 304)
Exercises 5 (Page 304)
Exercises 6 (Page 304)
Exercises 7 (Page 304)
Exercises 8 (Page 304)
Exercises 9 (Page 304)
Exercises 10 (Page 304)
Exercises 11 (Page 305)
Exercises 12 (Page 305)
Exercises 13 (Page 305)
Exercises 14 (Page 305)
Exercises 15 (Page 305)
Exercises 16 (Page 305)
Exercises 17 (Page 305)
Exercises 18 (Page 305)
Exercises 19 (Page 305)
Exercises 20 (Page 305)
Exercises 21 (Page 305)
Exercises 22 (Page 305)
Exercises 23 (Page 305)
Exercises 24 (Page 305)
Exercises 25 (Page 305)
Exercises 26 (Page 305)
Exercises 27 (Page 306)
Exercises 28 (Page 306)
Exercises 29 (Page 306)
Exercises 30 (Page 306)
Exercises 31 (Page 306)
Exercises 32 (Page 306)
Exercises 33 (Page 306)
Exercises 34 (Page 306)
Exercises 35 (Page 306)
Exercises 36 (Page 307)
Exercises 37 (Page 307)
Exercises 38 (Page 307)
Exercises 39 (Page 307)
Exercises 40 (Page 307)
Exercises 41 (Page 307)
Exercises 42 (Page 307)
Exercises 43 (Page 307)
Exercises 44 (Page 307)
45 engineering
46 engineering
47 engineering
48 engineering
Exercises 49 (Page 307)
Exercises 50 (Page 307)
Exercises 51 (Page 307)
Exercises 52 (Page 307)
Exercises 53 (Page 307)