Question 22·Easy·Lines, Angles, and Triangles
In the figure, lines and are parallel.
Which choice is the value of ?
When a transversal cuts two parallel lines, first classify the marked angles by position. If both angles are between the parallel lines on the same side of the transversal, they are same-side interior angles, so they add to . Then solve the simple subtraction to get the missing angle.
Hints
Locate both angles
Check whether both marked angles are between the two parallel lines and on the same side of the transversal.
Decide: equal or sum to 180?
Corresponding and alternate interior angles are equal, but same-side interior angles add to .
Set up one simple equation
If the angles are same-side interior, write and solve.
Desmos Guide
Compute the supplement
In the expression line, type 180-52.
Interpret the result
The value Desmos displays is the measure of (the angle that forms a supplementary pair with ).
Step-by-step Explanation
Use the same-side interior angles rule
The angle and the angle lie between the parallel lines and on the same side of the transversal, so they are same-side interior angles and are supplementary:
Solve for
Subtract from both sides:
So, the value of is 128.