Page 65 - Math Course 2 (Book 2)

Congruent Angels in Parallel Lines

Use an Auxiliary Line
m n
What is the measurement of ∠IGE?

6 A. 45
5 p
B. 48
q
7 C. 87

D. 93

m∠5 = m∠7 Definition of congruent angles

2x – 10 = x + 5 Substitution

Subtract x from each side and
x = 25
add 10 to each side.

Find y.
Since m || n, m∠5 ≅ m∠6 by the Alternate Exterior Answer
Angles Theorem.

Definition of congruent
m∠5 ≅ m∠6 angles
2x – 10 = 4(y – 25) Substitution
2(25) – 10 = 4 (y – 25)
Find Values of Variables
50 – 10 = 4y – 100
40 = 4y – 100 Simplify. ALGEBRA
If m∠1 = 9x + 6, m∠2 = 2(5x – 3) , m∠3 = 5y + 14,
140 = 4y Add 100 to each side. find x and y.

35 = y Divide each side by 4.
A. x = 9, y = 14
B. x = 12, y = 20
Answer x = 25 and y = 35 C. x = 10, y = 16
D. x = 14, y = 24

a b
Your Turn!

Determine Angle Measures 2 c

In the figure a || b and m∠18 = 42. Find m∠25. 1

A. 42 C 3 d
B. 84
C. 48 18 19 a
D. 138
20 21

22 23 b
24 25

Answer Answer

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