Question 252·Easy·Math

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Two adjacent angles form a straight angle. One angle measures 4 times the measure of the other. What is the measure, in degrees, of the smaller angle?

A linear pair is two adjacent angles that fill a straight angle, so their measures add to $180^\circ$ . Name the smaller angle $x$ and write the other as $4x$ , then use a Desmos regression to find $x$ . The key trap is giving the larger angle instead of the smaller one.

Hints

Hint 1
A straight angle measures $180^\circ$ . Adjacent angles sit side by side, so what equation says their measures fill that straight angle?
Hint 2
Let $x$ represent the smaller angle. Four times its measure is $4x$ , not $x+4$ . Which angle does the question ask you to find?

Step-by-step

Add the adjacent angles
Step 1
Write the angle-sum equation
Let $x$ be the smaller angle. The other is $4x$ because its measure is four times as large. The angles are adjacent and fill a straight angle, so their measures add to $180^\circ$ :
$x+4x=180.$
Step 2
Find the smaller angle in Desmos
Type $x_1+4x_1\sim180$ . This Desmos regression finds the unknown: $x_1$ replaces $x$ , and $\sim$ asks Desmos to match the two sides. Under PARAMETERS, Desmos shows $x_1=36$ . Since $x$ represents the smaller angle, its measure is $36^\circ$ . Choice B.

Lessons that teach this

SAT Geometry and TrigonometryBeginnerCoreUse line and angle relationships

Question 252·Easy·Math

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