In the figure shown, lines and are parallel. Two transversals intersect at point .
Which choice is the value of ?
Crossing transversals can form a triangle below their intersection, even when an angle is labeled above it. Vertical angles sit directly opposite each other at an intersection and are equal, so use the labeled angle to complete the lower triangle. Add that triangle’s angles to , then use a Desmos regression to find . The parallel lines aren’t needed for this route.
Hints
- Hint 1
At an intersection, vertical angles are directly across from each other, not side by side. The angle at inside the lower triangle sits across from the labeled angle above . What measure does it have?
- Hint 2
The labeled angles at and are inside triangle . A triangle’s interior angles add to . Add those two measures and the matching angle at .
Step-by-step
Complete the lower triangle
Step 1Find the lower angle at P
The transversals cross at , so the downward angle is directly opposite the labeled upward angle. Opposite angles at an intersection are vertical angles, and they’re equal: . Use the opposite angle at to complete triangle .
- Step 2
Write the triangle equation
The angles labeled at and are the other two angles inside triangle . A triangle’s three interior angles add to , so: . Use the downward angle at here; it has the same measure as the upward label.
- Step 3
Find the value of x
Type . Desmos uses for graphing, so and make a regression that finds the value making both sides equal. Under PARAMETERS, it shows . So the value of is . Choice C.