A cross street through parallel roads signals parallel-line angle relationships. Check whether the marked angles lie between the roads and on the same side of the cross street. If they do, they add to rather than match. Turn their labels into an equation, then use a Desmos regression to solve for the variable; don't judge the angles by how wide they look.
Hints
- Hint 1
A transversal is a line that crosses two other lines. Both marked angles are between the parallel roads. Are they on the same side of the cross street or on opposite sides?
- Hint 2
Same-side interior angles are between parallel lines on the same side of a transversal, and their measures add to . How can you put both labeled expressions into that sum?
Step-by-step
Use the same-side interior angle sum
Step 1Identify the angle relationship
At , the marked angle is below and left of . At , it's above and left of . They are same-side interior angles: both lie between the roads on the same side of the transversal, the line crossing them. Because the roads are parallel, same-side interior angles add to .
- Step 2
Write the angle-sum equation
Each label gives the measure of one marked angle, so put both expressions into the sum:
Don't set them equal. Equal alternate interior angles lie on opposite sides of the transversal.
- Step 3
Solve for the requested value
Type in Desmos. Use instead of and instead of so Desmos finds the unknown value rather than graphing the equation. Under PARAMETERS, it shows , so the value of is . Choice B.