Geometry / Unit 1: Foundations of Geometry
1.5 Angle Pairs
Notes
Some pairs of angles have special relationships that let you find missing measures.
- Complementary angles add to $90^\circ$. Supplementary angles add to $180^\circ$.
- Adjacent angles share a vertex and a side but no interior points.
- A linear pair is two adjacent angles whose outer sides form a line. They are supplementary.
- Vertical angles are opposite each other when two lines cross. Vertical angles are congruent.
- Example: the complement of $28^\circ$ is $62^\circ$; the supplement is $152^\circ$.
Practice
What is the supplement of a $47^\circ$ angle?
$180 - 47 = 133$.
Two lines intersect. One angle formed measures $72^\circ$. What is the measure of the angle vertical to it?
Vertical angles are congruent.
Two angles are complementary. One is twice the other. What is the larger angle?
$x + 2x = 90$, so $x = 30$ and the larger is $60^\circ$.
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