Lines and are parallel and are intersected by transversal , as shown.
The measure of one angle is , and the measure of another angle is .
Which choice is the value of ?
At a crossing, vertical angles sit opposite each other and are equal. A transversal crossing parallel lines also makes equal corresponding angles in the same corner at each crossing. Match the angle positions before writing an equation. Then use a Desmos regression to find the variable and calculate the requested angle. The trap is adding opposite angles as though they sit side by side.
Hints
- Hint 1
The two angles labeled with expressions sit across from each other at the upper crossing. Vertical angles are opposite angles formed by crossing lines, and their measures are equal. What equation does that give you?
- Hint 2
After finding , look at the corner occupied by at the lower crossing. Corresponding angles sit in the same corner at both crossings of parallel lines. Which upper angle matches ?
Step-by-step
Match the angles, then solve
Step 1Equate the opposite angles
At line , is above the line and left of ; is below the line and right of . They are vertical angles, so their measures are equal:
They aren't side by side, so don't add them to .
- Step 2
Find the value of
Type in Desmos. Use for the unknown and to tell Desmos to find where the two measures agree. Under PARAMETERS, Desmos shows , so .
- Step 3
Match to the upper angle
The angle is above and left of , the same corner as at line . Because and are parallel, these corresponding angles are equal: . Don't use the angle next to it, which has a different measure.
- Step 4
Calculate the requested angle
On a new Desmos line, type . Desmos prints , so measures , not the value of . Choice B.