7th Grade Angle Relationships and Equations Worksheet (PDF)

7th Grade math worksheet: Angle Relationships and Equations – Maths PDF

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This grade 7 angle relationships worksheet for 7th Grade covers angle relationships and equations (Common Core 7.G.B.5), with a free PDF to print.

These 20 problems practice supplementary, complementary, vertical, and adjacent angles, and simple equations for an unknown angle (Common Core 7.G.B.5). They start with the basic skill, move to different kinds of numbers and multistep work, and end with six word problems set in everyday situations such as shopping, sports, and travel.

Show every step of your work, and use the answer key only after you have tried each problem.

Grade 7 · Common Core State Standards: 7.G.B.5

Grade 7 angle relationships worksheet: exercises 1 to 10

Exercise 1 – Complement

Complementary angles.

Find the complement of a \(35^{\circ}\) angle.

Exercise 2 – Supplement

A linear pair.

Two angles form a linear pair, and one of them measures \(143^{\circ}\). Find the measure of the other angle.

Exercise 3 – Complement of a decimal

Find the complement of a \(72.5^{\circ}\) angle.

Exercise 4 – Vertical and adjacent

Two crossing lines.

Two lines cross. One angle measures \(48^{\circ}\). Find the vertical angle and each adjacent angle.

Exercise 5 – Complementary equation

Angles A and B are complementary. Angle A measures \(65^{\circ}\). Write and solve an equation to find angle B.

Exercise 6 – Supplementary equation

Angles C and D are supplementary. Angle D measures \(118^{\circ}\). Write and solve an equation to find angle C.

Exercise 7 – Two-step complement

Two complementary angles measure \((2x)^{\circ}\) and \(30^{\circ}\). Write and solve an equation to find x, then the first angle.

Exercise 8 – Supplementary expressions

Two supplementary angles measure \((3x+10)^{\circ}\) and \((x+30)^{\circ}\). Find x and both angles.

Exercise 9 – Vertical angle equation

Vertical angles.

Two vertical angles measure \((4x+5)^{\circ}\) and \(65^{\circ}\). Write and solve an equation to find x.

Exercise 10 – Ratio of complementary angles

Two complementary angles are in the ratio 2 : 3. Find each angle.

Exercises 11 and up

Exercise 11 – Three times as large

One of two supplementary angles is 3 times the other. Write and solve an equation to find both angles.

Exercise 12 – Linear pair

A linear pair.

A linear pair has measures \(x^{\circ}\) and \((2x+15)^{\circ}\). Find x and both angles.

Exercise 13 – Angles on a line

Three angles on a straight line measure \(40^{\circ}\), \(75^{\circ}\), and \(x^{\circ}\). Find x.

Exercise 14 – Angles around a point

Four angles around a point measure \(90^{\circ}\), \(120^{\circ}\), \(85^{\circ}\), and \(x^{\circ}\). Find x.

Exercise 15 – All four angles

Two lines cross and make an angle of \(70^{\circ}\). Find the other three angles.

Exercise 16 – Ladder

A ladder leans on a wall and makes a \(72^{\circ}\) angle with the ground. The wall and ground meet at a right angle. Find the angle the ladder makes with the wall.

Exercise 17 – Ramp

A ramp makes a \(15^{\circ}\) angle with the ground. Find the supplementary angle formed on the other side of the ramp along the ground line.

Exercise 18 – Scissors

The blades of a pair of open scissors form an angle of \(38^{\circ}\). Find the vertical angle on the other side of the pivot and the angle adjacent to the \(38^{\circ}\) angle.

Exercise 19 – Complementary expressions

Complementary expressions.

Two complementary angles measure \((2x-5)^{\circ}\) and \((x+20)^{\circ}\). Find x and both angles.

Exercise 20 – Pizza slices

A round pizza is cut into 8 equal slices. Find the angle at the center for one slice, and the supplement of that angle.

Key facts behind this grade 7 angle relationships worksheet

Key facts

Complementary angles add to \(90^{\circ}\); supplementary angles add to \(180^{\circ}\).
Angles on a straight line add to \(180^{\circ}\); angles around a point add to \(360^{\circ}\).
Vertical angles are equal.
Adjacent angles share a vertex and a side.
Write an equation from the relationship, solve it, and check the sum.

How to use this grade 7 angle relationships worksheet

Work through the exercises in order: they go from simple to challenging. Write every step on paper, then compare with the solutions page and redo any exercise you missed the next day.

Download the grade 7 angle relationships worksheet as a PDF with the button below and keep it with your notes.

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