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Common Core Math7th GradeGeometry

7.G.5: Solve for Unknown Angles

Also written as 7.G.B.5 and CCSS.MATH.CONTENT.7.G.B.5 · Cluster: Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.

All 24 7th Grade Math Standards

The Official Wording

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.

Common Core State Standards, Grade 7, Geometry · Read it at the source · Checked October 14, 2026

What 7.G.5 Means in Plain English

Seventh graders turn angle facts into equations. Two adjacent angles on a straight line, (3x + 15)° and (2x + 15)°, must add to 180°, so 5x + 30 = 180 and x = 30, giving 105° and 75°. Complementary angles add to 90°, and vertical angles are equal.

Most problems chain two facts: a straight line finds one angle, then vertical angles copy it across the crossing. In 8th grade the same reasoning covers parallel lines cut by a transversal and the angle sum of a triangle (8.G.5).

7.G.5 I Can Statements

  • I can name supplementary, complementary, vertical and adjacent angles.
  • I can write an equation for an unknown angle in a figure.
  • I can solve the equation and find every angle in the figure.

7.G.5 Worked Example

Two straight lines cross and two angles are given as expressions. One equation finds x, and vertical angles finish the job.

Problem

Two straight lines cross. One angle measures (3x + 15)°, and the angle beside it on the same line measures (2x + 15)°. Find x and all four angles.

Four angles where two lines cross
  1. The two angles are adjacent and together make a straight line, so they are supplementary: they add to 180°.(3x + 15) + (2x + 15) = 180
  2. Combine like terms.5x + 30 = 180
  3. Undo the steps in reverse: subtract 30, then divide by 5.5x = 150, so x = 30
  4. The question asks for angles, not x. Substitute.3(30) + 15 = 105°; 2(30) + 15 = 75°
  5. The other two angles are vertical to these, straight across the crossing, so they are equal to them.105°, 75°, 105°, 75°
Answerx = 30, and the four angles are 105°, 75°, 105° and 75°

Check it: The four angles around a point make a full turn: 105 + 75 + 105 + 75 = 360°. Any two neighbors should make a straight line, and 105 + 75 = 180.

Common Mistakes with 7.G.5

Stopping at x

x = 30, so the angle is 30°

Try this: Substitute x back into each expression before answering: the question asks for angles, and 3(30) + 15 = 105°.

Using 180° for complementary angles

Complementary angles x and 2x: 3x = 180, so x = 60

Try this: Picture the corner of a page: complementary angles fill a right angle, so 3x = 90 and x = 30.

Adding vertical angles to 180°

Vertical angles 4x and 100°: 4x + 100 = 180, so x = 20

Try this: Set vertical angles equal, 4x = 100 and x = 25; only angles that share a straight line add to 180°.

Where 7.G.5 Fits

Comes Before4.MD.7Angle measure is additive: the parts of an angle add to the whole.6.EE.7Solve one-step equations like 5x = 150.
Alongside7.EE.4Write and solve two-step equations like 5x + 30 = 180.7.G.2Draw triangles, where two angles settle the third.
Comes Next8.G.5Angles formed by parallel lines and a transversal, and the triangle angle sum.
HSG-CO.9Prove theorems about lines and angles, including that vertical angles are equal.

Practice 7.G.5

Quick Check

  1. Two angles are complementary. One is 28°. What is the other?
  2. Two adjacent angles on a straight line measure x° and (x + 40)°. Find both.
  3. Two lines cross. One angle is (5x − 10)° and the angle vertical to it is 65°. Find x.

7.G.5: Other Names

7.G.57.G.B.5CCSS.MATH.CONTENT.7.G.B.5

Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved. Official wording from the Common Core State Standards PDFs at corestandards.org, last checked October 14, 2026. The explanation, I can statements, example, mistakes and practice on this page are EMStudio’s own, written beside the official wording. They are not part of the standard.