---
title: "7.GSR.5: Angles, Circles & 3D Figures (Georgia Mathematics standard)"
code: 7.GSR.5
cite_as: Georgia Standards of Excellence, Mathematics, 7.GSR.5
subject: math
grades:
  - grade-7
language: en
canonical_url: https://georgiahomeroom.org/standards/code/7.GSR.5
md_url: https://georgiahomeroom.org/standards/code/7.GSR.5.md
alternate_language_url: https://georgiahomeroom.org/es/standards/code/7.GSR.5.md
source_url: https://case.georgiastandards.org/ims/case/v1p1/CFDocuments/e9dd7229-3558-4df2-85c6-57b8938f6180
source_last_changed: 2024-10-09
data_built: 2026-09-18
publisher: Georgia Homeroom, a free public-interest project of Georgia Civic Data. Not affiliated with or endorsed by the Georgia Department of Education or any school district.
up: https://georgiahomeroom.org/standards/math/grade-7.md
index: https://georgiahomeroom.org/standards/index.md
---

# 7.GSR.5: Angles, Circles & 3D Figures

Solve practical problems involving angle measurement, circles, area of circles, surface area of prisms and cylinders, and volume of cylinders and prisms composed of cubes and right prisms.

- Subject: Mathematics
- Appears in: Grade 7, https://georgiahomeroom.org/standards/math/grade-7.md

## Expectations

- **7.GSR.5.1**: Measure angles in whole nonstandard units.
- **7.GSR.5.2**: Measure angles in whole number degrees using a protractor.
- **7.GSR.5.3**: Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve equations for an unknown angle in a figure.
- **7.GSR.5.4**: Explore and describe the relationship between pi, radius, diameter, circumference, and area of a circle to derive the formulas for the circumference and area of a circle.
- **7.GSR.5.5**: Given the formula for the area and circumference of a circle, solve problems that exist in everyday life.
- **7.GSR.5.6**: Solve realistic problems involving surface area of right prisms and cylinders.
- **7.GSR.5.7**: Describe the two-dimensional figures (cross sections) that result from slicing three-dimensional figures, as in the plane sections of right rectangular prisms, right rectangular pyramids, cones, cylinders, and spheres.
- **7.GSR.5.8**: Explore volume as a measurable attribute of cylinders and right prisms. Find the volume of these geometric figures using concrete problems.

## Georgia Milestones coverage

- Mathematics Grade 7 (EOG). Geometric & Spatial Reasoning. Solve practical problems involving angle measurement, circles, area of circles, surface area of prisms and cylinders, and volume of cylinders and prisms composed of cubes and right prisms. (about 16% of the test; 9 points)

## What mastery looks like

Georgia's Achievement Level Descriptors. The levels are cumulative: each includes the ones before it. Proficient is on grade level.

- **Beginning**: Determine the measure of an angle with a whole, nonstandard unit. Identify supplementary, complementary, vertical, and adjacent angles.
- **Developing**: Given a circle divided into wedges of equal size, make a comparison. Determine the measure of an angle, in whole-number degrees, using a protractor. Solve a problem by using facts about supplementary, complementary, vertical, and adjacent angles. Determine the circumference and area of a circle. Determine the surface area of right prisms and cylinders. Determine the volumes of cylinders and right prisms.
- **Proficient**: Determine the measure of an angle within a figure, in whole-number degrees, using a protractor. Solve a multi-step problem by using facts about supplementary, complementary, vertical, and adjacent angles. Solve a realistic problem involving the area or circumference of a circle. Solve a realistic problem involving the surface areas of a right prism and a cylinder. Identify the two-dimensional cross sections that result from horizontally or vertically slicing (limited to horizontal and vertical slices) right rectangular prisms, right rectangular pyramids, cones, cylinders, and spheres. Solve multi-step problems involving the volumes of cylinders and right prisms.
- **Distinguished**: Solve a multi-step problem with multiple relationships between supplementary, complementary, vertical, and adjacent angles. Solve multi-step, realistic problems involving the areas and circumferences of circles and the surface areas and volumes of prisms and cylinders.

## The same standard across grades

- Grade 6, 6.GSR.5: Solve relevant problems involving area, surface area, and volume. https://georgiahomeroom.org/standards/code/6.GSR.5.md
- **Grade 7, 7.GSR.5 (this standard)**: Solve practical problems involving angle measurement, circles, area of circles, surface area of prisms and cylinders, and volume of cylinders and prisms composed of cubes and right prisms.

Source: Georgia Standards of Excellence, published by the Georgia Department of Education at case.georgiastandards.org.