# 8.5 - Angles

8.5  The student will use the relationships among pairs of angles that are vertical angles, adjacent angles, supplementary angles, and complementary angles to determine the measure of unknown angles.

### 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

2016 VDOE Curriculum Framework - 8.5 Understanding

·  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

·  8.51  Identify and describe the relationship between pairs of angles that are vertical, adjacent, supplementary, and complementary.

·  8.52  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