What you’ll learn
Write equations for unknown angles.
Key idea
Opposite vertical angles require equal measures; complementary angles require their sum to be90°.
The relationship determines equality versus sum; retain the complete angle label, not only its variable term.
Worked example
Enter the exact value or ordered values in the format requested below.
An unknown angle is labeled (2x+8)°, with a complementary partner of 78°. For vertical, two straight lines intersect; for complementary, their total is90°. Create the relationship equation in x, not a numeric solution.
- The geometric constraint is that complementary measures sum to90°.
- Translate the entire label (2x+8)° with known 78°: 2x+8+78=90; solving gives x=2.
Answer: 2x+8+78=90
Quick Check
Choose which candidate representation satisfies the requirements of 'Write equations for unknown angles' and justify the choice.
Unknown angle (2x+5)° and known angle 13° are vertical. Compare A:2x+5=13; B:2x+5+13=180; C:2x=13. Select and justify the geometry model.