Angle A and Angle B are supplementary angles. If the measure of Angle A is (6x - 10)^\circ… — Armed Services Vocational Aptitude Battery (ASVAB)

Angle $A$ and Angle $B$ are supplementary angles. If the measure of Angle $A$ is $(6x - 10)^\circ$ and the measure of Angle $B$ is $(4x + 30)^\circ$ , what is the measure of Angle $A$ ?

A
$106^\circ$
B
$32^\circ$
$86^\circ$ Answer
D
$122^\circ$

Answer

The measure of Angle

A

86^\circ

The correct answer is

86^\circ

. Because Angle

A

and Angle

B

are supplementary, their measures add up to

180^\circ

. Setting up the equation

(6x - 10) + (4x + 30) = 180

and combining like terms yields

10x + 20 = 180

. Solving for

x

gives

x = 16

. Substituting

16

into the expression for Angle

A

(

6x - 10

) results in

6(16) - 10 = 86^\circ

Step-by-Step Solution

Set up an equation based on the definition of supplementary angles.

(6x - 10) + (4x + 30) = 180

Supplementary angles always have a combined sum of

180^\circ

Combine like terms on the left side of the equation.

10x + 20 = 180

Grouping the

x

terms (

6x + 4x

) and constant terms (

-10 + 30

) simplifies the algebraic expression.

Isolate the variable term by subtracting

20

from both sides.

10x = 160

This removes the constant from the variable side, beginning the process of solving for

x

Divide by

10

to solve for

x

x = 16

Dividing both sides by the coefficient isolates

x

Substitute the value of

x

back into the expression for Angle

A

6(16) - 10 = 96 - 10 = 86^\circ

The question asks for the specific measure of Angle

A

, not just the value of the variable

x

Key Concept

Supplementary angles are two angles whose measures add up to

180^\circ

. To find unknown measures, set the sum of their algebraic expressions equal to

180

, solve for the variable, and substitute it back into the target expression.

Question

Answer

Step-by-Step Solution

Key Concept

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