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Big Ideas Math Integrated I, 2016

BI

Big Ideas Math Integrated I, 2016 View details

5. Proving Geometric Relationships

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Exercise 12 Page 483

By the Vertical Angles Congruence Theorem we know that vertical angles are congruent.

$x = 13$
$y = 20$

Practice makes perfect

Looking at the figure, we can identify two pairs of vertical angles. The measure of each pair is given as algebraic expressions. One pair is written in terms of

x

and one pair is in terms of

y .

Vertical Angles 1 : Vertical Angles 2 : 4 x^{\circ} and (6 x - 26)^{\circ} (6 y + 8)^{\circ} and (7 y - 12)^{\circ}

By the Vertical Angles Congruence Theorem, we know that vertical angles are congruent. Therefore, we can equate the given expressions and solve for

x

and

y .

Let's find the value of

x

first.

4 x = 6 x - 26

▼

Solve for

x

$LHS - 4 x = RHS - 4 x$

0 = 2 x - 26

$LHS + 26 = RHS + 26$

26 = 2 x

$LHS / 2 = RHS / 2$

13 = x

Rearrange equation

x = 13

Now let's do the same thing for

y .

7 y - 12 = 6 y + 8

▼

Solve for

y

$LHS - 6 y = RHS - 6 y$

y - 12 = 8

$LHS + 12 = RHS + 12$

y = 20

Subchapter links

Communicate Your Answer p.477

Monitoring Progress p.478-482

Exercises p.483-486