Question 372·Easy·Math

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Two straight lines intersect, forming four angles. One of the acute angles measures $38^\circ$ . What is the measure of one of the obtuse angles formed by the intersection?

Two lines crossing give linear pairs: neighboring angles on a straight line that add to $180^\circ$ . To find the angle beside a given one, subtract its measure from $180^\circ$ ; that one subtraction needs no Desmos. Opposite angles have equal measures, so copying the given angle finds the one across from it, not the differently sized angle beside it.

Hints

Hint 1
A linear pair is two angles beside each other whose outside sides form a straight line. Their measures add to $180^\circ$ . Write a sum using the given angle and an angle beside it.
Hint 2
An obtuse angle measures more than $90^\circ$ . The angle directly across from the given angle has the same measure, so look beside it instead. What must you subtract from the straight-angle total?

Step-by-step

Use a straight angle
Step 1
Write the neighboring angles' sum
No Desmos needed. A straight-angle fact leaves one subtraction. The $38^\circ$ angle and an angle beside it form a linear pair: two neighboring angles whose outside sides make a straight line. Their measures add to $180^\circ$ . If $x$ is the measure of the neighboring angle, then $38+x=180$ .
Step 2
Find the obtuse angle
Subtract $38$ from both sides:
$\begin{aligned}x&=180-38\x&=142.\end{aligned}$
The angle beside the given one measures $142^\circ$ . It is obtuse, meaning greater than $90^\circ$ , so it answers the question. Choice C.

Lessons that teach this

SAT Geometry and TrigonometryBeginnerCoreUse line and angle relationships

Question 372·Easy·Math

Strategy

Hints

Step-by-step

Lessons that teach this

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Strategy

Hints

Step-by-step

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