Question 35·Medium·Lines, Angles, and Triangles
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 ?
When parallel lines are cut by a transversal, first use the easiest relationship at a single intersection (often vertical angles or a linear pair) to solve for the variable. Only after the variable is found should you move to the other intersection and use corresponding or alternate interior positions to transfer the angle measure to the requested angle.
Hints
Look at the two expressions on line
At the upper intersection, decide what relationship the angles labeled and have based on their positions.
Solve for the variable first
Write an equation using those two angle expressions and solve for .
Match the position of
Compare where is located at the lower intersection to where is located at the upper intersection (for example, upper-left, upper-right, and so on).
Desmos Guide
Find by graphing the two expressions
Enter and (use a different variable name if needed, such as , in place of ).
Locate the intersection
Click the intersection point of the two lines. The -coordinate is the value of that makes the angle measures equal.
Compute from the corresponding angle expression
In Desmos, evaluate at the intersection value of (for example, by entering and using the intersection -value). The result is .
Step-by-step Explanation
Set vertical angles equal
At the intersection on line , the angles labeled and are vertical angles, so they are equal:
Solve for
Solve the equation:
Use corresponding angles to find
Angle is in the same relative position (upper-left) at the lower intersection as the angle is at the upper intersection, so they are corresponding angles and have equal measures.
Compute:
Therefore, the value of is 60.