Page 94 - Math Course 1 (Book 2)

Relationships in Angles

B. Name two acute vertical angles.
Your Turn!
There are four acute angles shown. There is one
pair of vertical angles. Use Algebra to Find Angle Measures

The acute vertical angles are
Answer
∠VZY and ∠XZW

Angle Measure

Examples

ALGEBRA
Find the measures of two supplementary angles if
the measure of one angle is 6 less than f ve times
the other angle.

Explore The problem relates the measures of two
supplementary angles. You know that the
sum of the measures of supplementary
angles is 180. A. Name two adjacent angles whose sum is less
than 90.
Plan Draw two f gures to represent the angles.
A. ∠CAD and ∠DAE
B. ∠FAE and ∠FAN
C. ∠CAB and ∠NAB
D. ∠BAD and ∠DAC
Answer

Let the measure of one angle be x. B. Name two acute vertical angles.
If m ∠A = x then ∠B = 5x – 6.
A. ∠BAN and ∠EAD
Solve m∠A + m∠B = 180 Given B. ∠BAD and ∠BAN
m∠A = x, then C. ∠BAC and ∠CAE
x + (5x – 6) = 180
m∠B = 5x – 6 D. ∠FAN and ∠DAC
6x – 6 = 180 Simplify. Answer

6x = 186 Add 6 to each side. Angle Measure
x = 31 Divide each side by 6.
ALGEBRA Find the measures of two complementa-
Use the value of x to find each angle measure. ry angles if one angle measures six degrees less
m� A = x m� = 5x – 6 than f ve times the measure of the other.
m� A = 31 m� = 5(31) – 6 or 149
A. 1°, 1°
Examine Add the angle measures to verify that the B. 21°, 111°
angles are supplementary. C. 16°, 74°
D. 14°, 76°
m∠A + m∠B = 180
31 + 149 = 180 Answer
180 = 180

Answer 31, 149

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