What you’ll learn
Use vertical-angle relationships.
Key idea
Vertical opposite angles are equal; it is adjacent linear pairs that sum to180°.
Opposite vertical angles are equal, not generally supplementary; adjacent linear pairs are a different relationship.
Worked example
Enter the exact value or ordered values in the format requested below.
Two straight lines intersect. One angle is 13°; its vertical opposite angle is labeled (2x+7)°. Enter the opposite angle measure, not x.
- Two straight lines intersect; opposite angles are vertical and equal, so unknown measure is 13°.
- The label gives 2x+7=13; x=(13-7)/2=3.
Answer: 13
Quick Check
Evaluate a worked attempt at use vertical-angle relationships, identify the first invalid step, and provide the correction.
Opposite angles at two intersecting straight lines are 17° and (2x+5)°. Step1 identifies vertical angles. Step2 sets their sum to180° and unknown measure=163°. Locate the first invalid step and correct the measure.