7th Grade Angle Relationships and Equations Test Solutions and Scoring (PDF)

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

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This grade 7 angle relationships test 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 and scoring guide to grade the angle relationships test. Each solution shows the full work, and the scoring note explains how the points are awarded. Give partial credit for correct steps even when the final answer is wrong.

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

Grade 7 angle relationships test answers: worked solutions

Question 1 – Complementary [2 pts]

The angles are complementary: \(28+x=90\), so \(x=62\).

x = 62; complementary

28° + 62° = 90°.

Scoring: 1 point for the relationship; 1 point for x.

Question 2 – Supplementary [2 pts]

\(x+133=180\), so \(x=47\).

x = 47; a linear pair

Scoring: 1 point for the equation; 1 point for x with the name.

Question 3 – Crossing lines [2 pts]

a is adjacent to 54°: \(180-54=126^{\circ}\). b is vertical to the 54° angle: \(54^{\circ}\). c is vertical to a: \(126^{\circ}\).

a = 126°, b = 54°, c = 126°

All four angles.

Scoring: 1 point for two correct angles; 1 point for the third and the explanation.

Question 4 – Complementary expressions [2 pts]

\(5x+30=90\), so \(x=12\).

\(3(12)+6=42\) and \(2(12)+24=48\).

x = 12; \(42^{\circ}\) and \(48^{\circ}\)

Scoring: 1 point for x; 1 point for both angles.

Question 5 – Vertical angles equation [2 pts]

\(5x-8=52\), \(5x=60\), \(x=12\).

x = 12

Scoring: 1 point for the equation; 1 point for x.

Question 6 – Around a point [2 pts]

\(110+95+60+x=360\), so \(265+x=360\) and \(x=95\).

\(95^{\circ}\)

Scoring: 1 point for the equation (sum 360); 1 point for x.

Question 7 – Ratio [2 pts]

\(4k+5k=180\), \(9k=180\), \(k=20\).

Angles: \(80^{\circ}\) and \(100^{\circ}\).

\(80^{\circ}\) and \(100^{\circ}\)

Scoring: 1 point for the equation; 1 point for both angles.

Question 8 – Linear pair equation [3 pts]

\(x+10+3x=180\).
\(4x+10=180\), \(4x=170\), \(x=42.5\).
\(42.5+10=52.5^{\circ}\) and \(3(42.5)=127.5^{\circ}\).

The two angles.

Scoring: 1 point for each part.

Question 9 – Crossing roads [3 pts]

The other angles are 115, 65, and 115 degrees.
The two 65-degree angles are vertical angles, and the two 115-degree angles are vertical angles.
They are adjacent and form a straight line, so they add up to 180 degrees.

All four angles.

Scoring: 1 point for each part.

Total score

Total

20 points

Key facts behind this grade 7 angle relationships test 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 test answers

Score your test with the point values shown for each question. Then read the worked solution of every question where you lost points and note the method to review.

All Grade 7 chapters: Grade 7 math.

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