An aviation engineer is evaluating the intersection of two flight paths on a radar display… — Armed Services Vocational Aptitude Battery (ASVAB)

An aviation engineer is evaluating the intersection of two flight paths on a radar display. The flight paths are represented by two straight intersecting lines. Two adjacent angles formed by this intersection have measures of $(8x)^\circ$ and $(2x + 10)^\circ$ . What is the measure of the smaller of these two adjacent angles?

A
$26^\circ$
B
$28^\circ$
C
$34^\circ$
$44^\circ$ Answer

Answer

The smaller angle measures

44^\circ

Adjacent angles on a straight line form a linear pair and are supplementary, meaning their sum is 180 degrees. Setting up the equation 8x + 2x + 10 = 180 simplifies to 10x + 10 = 180. Subtracting 10 from both sides leaves 10x = 170, and dividing by 10 yields x = 17. Substituting x back into the expressions gives angle measures of 8(17) = 136 degrees and 2(17) + 10 = 44 degrees. The question asks for the smaller angle, which is 44 degrees.

Step-by-Step Solution

Recognize that adjacent angles formed by intersecting lines create a linear pair.

The angles are supplementary, meaning their sum is

180^\circ

This geometric rule provides the basis for setting up the equation.

Set up an equation representing the sum of the two angles.

8x + (2x + 10) = 180

This translates the geometric relationship into an algebraic expression.

Combine the like terms on the left side of the equation.

10x + 10 = 180

Simplifying the equation is the first step in isolating the variable x.

Solve for x by subtracting 10 from both sides and then dividing by 10.

10x = 170 \Rightarrow x = 17

These standard algebraic operations isolate x and determine its exact value.

Substitute x = 17 back into both original expressions to find the angle measures.

8(17) = 136^\circ

and

2(17) + 10 = 34 + 10 = 44^\circ

The question asks for a specific angle measure, not the variable x.

Identify the smaller of the two calculated angles.

44^\circ

The prompt specifically requests the measure of the smaller angle.

Key Concept

Linear pairs of angles form a straight line and are supplementary, meaning they add up to 180 degrees.

Estimated Time:1m 15s

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