Pre-Algebra
Geometry
Angle relationships (supplementary, complementary, vertical)
20 practice questions
0 video lessons
Theory + worked examples
Angle Relationships
Texas Pre-Algebra (TEKS) • Standard 7.11(C) • Geometry
Angle Relationships is a topic in Geometry in the Texas Essential Knowledge and Skills. It is aligned to Standard 7.11(C), which requires students to use complementary, supplementary, and vertical angle relationships.
Complementary angles sum to \(90^\circ\), supplementary to \(180^\circ\), and vertical angles are equal.
Theory
Angle pairs:
- Complementary: sum to \(90^\circ\).
- Supplementary: sum to \(180^\circ\).
- Vertical angles (across an intersection) are equal.
Set up an equation from the relationship to solve for an unknown angle.
Complementary and supplementary.
Angle relationships.
The sums:
\[\text{comp: }a+b=90^\circ,\quad \text{supp: }a+b=180^\circ\]
Vertical angles are always congruent.
How to use angle relationships
- Identify the relationship.
- Write an equation from the sum or equality.
- Solve for the unknown.
- Check the angle is reasonable.
Example 1 — Complement
Find the complement of \(35^\circ\).
Solution
Subtract from \(90\).
| \(90-35\) | \(=\) | \(55^\circ\) |
Example 2 — Supplement
Find the supplement of \(110^\circ\).
Solution
Subtract from \(180\).
| \(180-110\) | \(=\) | \(70^\circ\) |
Example 3 — Vertical
Two vertical angles: one is \(40^\circ\). Find the other.
Solution
Vertical angles are equal.
| \(40^\circ\) |
Example 4 — Solve
Angles \(x\) and \(2x\) are complementary. Find \(x\).
Solution
They sum to \(90\).
| \(3x\) | \(=\) | \(90\) |
| \(x\) | \(=\) | \(30^\circ\) |
Common pitfalls
Complementary is \(90\), supplementary is \(180\).
Vertical angles are equal, not supplementary.
Write an equation to solve.
Frequently asked questions
What are complementary angles?
Two angles summing to \(90^\circ\).
What are supplementary angles?
Two angles summing to \(180^\circ\).
What are vertical angles?
Opposite angles at an intersection; they are equal.
Complement of \(35^\circ\)?
\(55^\circ\).
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