7th Grade Angle Relationships and Equations Worksheet Solutions (PDF)

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

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

Use this answer key to check your work on the angle relationships worksheet. Every solution shows the steps, and the final answer appears in bold. If your answer is different, compare each step and look for the first place where the work changes.

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

Grade 7 angle relationships answers: exercises 1 to 10

Exercise 1 – Complement

\(90-35=55\)

\(55^{\circ}\)

35° + 55° = 90°.

Exercise 2 – Supplement

A linear pair is supplementary: \(180 – 143 = 37\).

\(37^{\circ}\)

37° + 143° = 180°.

Exercise 3 – Complement of a decimal

\(90-72.5=17.5\)

\(17.5^{\circ}\)

Exercise 4 – Vertical and adjacent

Vertical angles are equal: \(48^{\circ}\).

Adjacent angles form a linear pair: \(180-48=132\).

vertical \(48^{\circ}\); adjacent \(132^{\circ}\)

All four angles.

Exercise 5 – Complementary equation

\(x+65=90\), so \(x=25\).

\(25^{\circ}\)

Exercise 6 – Supplementary equation

\(x+118=180\), so \(x=62\).

\(62^{\circ}\)

Exercise 7 – Two-step complement

\(2x+30=90\).

\(2x=60\), so \(x=30\).

The first angle is \(2(30)=60^{\circ}\).

x = 30; \(60^{\circ}\)

Exercise 8 – Supplementary expressions

\(3x+10+x+30=180\), so \(4x+40=180\).

\(4x=140\), \(x=35\).

Angles: \(3(35)+10=115\) and \(35+30=65\).

x = 35; \(115^{\circ}\) and \(65^{\circ}\)

The angles are 65° and 115°.

Exercise 9 – Vertical angle equation

Vertical angles are equal: \(4x+5=65\).

\(4x=60\), so \(x=15\).

x = 15

Exercise 10 – Ratio of complementary angles

Let the angles be \(2k\) and \(3k\). Then \(5k=90\), so \(k=18\).

\(2(18)=36\) and \(3(18)=54\).

\(36^{\circ}\) and \(54^{\circ}\)

Exercises 11 and up

Exercise 11 – Three times as large

\(x+3x=180\), so \(4x=180\) and \(x=45\).

The other angle is \(3(45)=135\).

\(45^{\circ}\) and \(135^{\circ}\)

Exercise 12 – Linear pair

\(x+2x+15=180\), so \(3x=165\) and \(x=55\).

The other angle is \(2(55)+15=125\).

x = 55; \(55^{\circ}\) and \(125^{\circ}\)

The linear pair: 55° and 125°.

Exercise 13 – Angles on a line

\(40+75+x=180\), so \(115+x=180\) and \(x=65\).

\(65^{\circ}\)

Exercise 14 – Angles around a point

\(90+120+85+x=360\), so \(295+x=360\) and \(x=65\).

\(65^{\circ}\)

Exercise 15 – All four angles

Vertical: \(70^{\circ}\).

The other two: \(180-70=110^{\circ}\) each.

\(70^{\circ}\), \(110^{\circ}\), \(110^{\circ}\)

All four angles.

Exercise 16 – Ladder

The ladder, wall, and ground form a right triangle, and the angles of a triangle add up to \(180^{\circ}\).

\(90+72+x=180\), so \(x=18\).

\(18^{\circ}\)

Exercise 17 – Ramp

\(180-15=165\)

\(165^{\circ}\)

Exercise 18 – Scissors

Vertical: \(38^{\circ}\). Adjacent: \(180-38=142^{\circ}\).

\(38^{\circ}\) and \(142^{\circ}\)

Exercise 19 – Complementary expressions

\(2x-5+x+20=90\), so \(3x+15=90\).

\(3x=75\), \(x=25\).

Angles: \(2(25)-5=45\) and \(25+20=45\).

x = 25; \(45^{\circ}\) and \(45^{\circ}\)

Exercise 20 – Pizza slices

The full turn is \(360^{\circ}\): \(360\div 8=45\).

Supplement: \(180-45=135\)

\(45^{\circ}\); \(135^{\circ}\)

Eight slices of 45° each.

Key facts behind this grade 7 angle relationships answers

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 answers

Cover each solution, solve the exercise again, then uncover it and compare every line. If your answer differs, find the first step that changed and redo the exercise from there.

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