#### Math - 2018-19

# 8.5 - Angles

8.5The student willusethe relationships among pairs of angles that are vertical angles, adjacent angles, supplementary angles, and complementary angles todeterminethe measure of unknown angles.

*Adopted: 2016*

### BIG IDEAS

- I can make a double bank shot in an air hockey game, build a
handrail on a downhill slope, determine the angle of the sun based on colors in
a rainbow, and correctly paint the lines in a parking lot.

- I will be able to find angle measurements and relationships by using patterns and the positions of angles formed by parallel lines and a transversal.

### UNDERSTANDING THE STANDARD

· Vertical angles are a pair of nonadjacent angles formed by two intersecting lines. Vertical angles are congruent and share a common vertex.

· Complementary angles are any two angles such that the sum of their measures is 90°.

· Supplementary angles are any two angles such that the sum of their measures is 180°.

· Complementary and supplementary angles may or may not be adjacent.

· Adjacent angles are any two non-overlapping angles that share a common ray and a common vertex.

### ESSENTIALS

- How are vertical,
adjacent, complementary and supplementary angles related?

Adjacent angles are any two non-overlapping angles that share a common side and a common vertex. Vertical angles will always be nonadjacent angles. Supplementary and complementary angles may or may not be adjacent.

**The student will use problem solving, mathematical
communication, mathematical reasoning, connections, and representations to**

·
8.5_{1}** Identify**
and **describe** the relationship
between pairs of angles that are vertical, adjacent, supplementary, and
complementary.

·
8.5_{2}** Use**
the relationships among supplementary, complementary, vertical, and adjacent
angles to **solve** problems, including
practical problems, involving the measure of unknown angles.

### KEY VOCABULARY

angle, degree, intersecting lines, vertical angles, supplementary
angles, complementary angles, adjacent angles, parallel lines, transversal

*Updated: Nov 20, 2018*