7.G.5
2012
Domain: Geometry
Cluster: Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
Standards: 7.G.5. Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to
write and solve simple equations for an unknown angle in a figure.
Essential Questions
Enduring Understandings
Activities, Investigation, and Student Experiences

What angles are
measured in the real
world?
 Geometry and spatial sense
offer ways to interpret and
reflect physical environment.
Example:
Write and solve an equation to find the measure of angle x.

Why are angle
measurements
important?
 Analyzing geometric
relationships develops
reasoning and justification
skills.
Content Statements

Use understandings of
angles and deductive
reasoning to write and
solve equations.

Use properties of
supplementary,
complementary,
vertical and adjacent
angles to solve simple
equations for unknown
angles in a figure.

Write and solve
equations based on a
diagram of intersecting
lines with some known
Solution:
Find the measure of the missing angle inside the triangle (180 –
90 – 40), or 50°.
The measure of angle x is supplementary to 50°, so subtract 50
from 180 to get a measure of 130° for x.
Example:
Find the measure of angle x.
Solution:
First, find the missing angle measure of the bottom triangle (180
– 30 – 30 = 120). Since the 120 is a vertical angle to x, the
measure of x is also 120°.
7.G.5
2012
angle measures.

Solve multi-step
equations involving
angle measures.

Solve real-life
mathematical problems
involving angles.
Assessments
Skill-based Task
Solve for x and y.
Example:
Find the measure of angle b. Note: Not drawn to scale.
Solution:
Because, the 45°, 50° angles and b form a supplementary angle,
the measure of angle b would be 85°. The measures of the
angles of a triangle equal 180° so 75° + 85°+ a = 180°. The
measure of angle a would be 20°.
Activity:
 Use patty paper or a reflecting device (mira) to explore
relationships among the measures of angles formed by
intersecting lines.
Problem Task:
If 𝑚∠𝐵=102° and 𝑚∠𝐿=120°, find every other angle
measure, explaining how you found each.

Draw two intersecting lines. Measure one angle and find
the measures of the others without measuring.

Provide explicit examples of supplementary,
complementary, vertical, and adjacent angles and
demonstrate their relationships, including adjacent
angles that are neither supplementary nor
complementary.
7.G.5
2012
Problem of the Month:
What’s Your Angle?
Equipment Needed:
Teacher Resources:
Pen/Pencil
 http://nlvm.usu.edu
Paper
 http://illuminations.nctm.org/
Ruler
 http://insidemathematics.org/index.php/7th-grade
Reference books
 http://www.ncpublicschools.org/docs/acre/standards/c
ommon-core-tools/unpacking/math/7th.pdf
Internet
Overhead
Graphing calculator
Interactive whiteboard
Online Activities
Appropriate manipulatives
 http://www.schools.utah.gov/CURR/mathsec/Core/7th
-Grade-Core/7G2.aspx