Question 240·Easy·Math

0 / 2000

Two hiking trails intersect at point $P$ , forming four angles. One of the angles measures $47^\circ$ . The angle adjacent to this $47^\circ$ angle that forms a straight line with it is labeled $y^\circ$ . What is the value of $y$ ?

At intersecting lines, a linear pair is two touching angles whose outside rays form a straight line. That straight line is the cue to add their measures to $180^\circ$ , then subtract the known angle. Don’t use the rule for vertical angles: those sit across the intersection, not beside each other.

Hints

Hint 1
A linear pair consists of two angles that share a side while their other sides point in opposite directions. Do the outer rays of the labeled angles make a straight line?
Hint 2
Angles that fill a straight line add to $180^\circ$ . Add $y$ and the known angle, then subtract the known angle to find what remains.

Step-by-step

Use the straight angle
Step 1
Write the angle equation
No Desmos needed. The missing angle takes one subtraction. The $47^\circ$ angle and $y^\circ$ share a side, and their other sides point in opposite directions. They form a linear pair. Angles that fill a straight line add to $180^\circ$ , so:
$y+47=180.$
Step 2
Find the missing angle
Subtract $47$ from both sides:
$y=180-47.$
Finish the subtraction:
$y=133.$
The angle labeled $y^\circ$ measures $133^\circ$ . Choice B.

Lessons that teach this

SAT Geometry and TrigonometryBeginnerCoreUse line and angle relationships

Question 240·Easy·Math

Strategy

Hints

Step-by-step

Lessons that teach this

Study Hints

Strategy

Hints

Step-by-step

Lessons that teach this