Question 288·Easy·Math

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In the figure, lines $p$ and $q$ are parallel.

Which choice is the value of $b$ ?

Parallel lines crossed by a slanted line are a cue to check where the marked angles sit. Same-side interior angles lie between the parallel lines on the same side of that crossing line, so they add to $180^\circ$ . Write that relationship as an equation, then use a Desmos regression to find the missing angle. Don't set the angles equal merely because the lines are parallel.

Hints

Hint 1
A transversal is a line that crosses both parallel lines. Check the positions of the marked angles: are they between the lines and on the same side of the transversal?
Hint 2
Same-side interior angles add to $180^\circ$ when the lines are parallel. Add the two marked measures, rather than setting them equal. What value would make their sum $180$ ?

Step-by-step

Use same-side interior angles
Step 1
Turn the angle positions into an equation
The $52^\circ$ angle is below $p$ , and the $b^\circ$ angle is above $q$ . Both are between the parallel lines and on the same side of the diagonal transversal, the line crossing them. Same-side interior angles add to $180^\circ$ , so $52+b=180$ .
Step 2
Find the missing angle
Type $52+b\sim180$ . The regression asks Desmos to find $b$ that makes the equation true. Under PARAMETERS, it shows $b=128$ , so the angle labeled $b^\circ$ measures $128^\circ$ . Choice C.

Lessons that teach this

SAT Geometry and TrigonometryBeginnerCoreUse line and angle relationships

Question 288·Easy·Math

Strategy

Hints

Step-by-step

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Strategy

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Step-by-step

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