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Grade 7 Math · Angles and Geometric Constructions

Grade 7 Angles and Geometric Constructions Practice Test

Build Grade 7 Math skills with five 10-question practice tests on angle relationships, parallel lines, constructions, triangles, and quadrilaterals.

Angles and Geometric Constructions Practice Tests

These Grade 7 Math practice tests help students solve angle relationships and understand classical geometric constructions. Students work with complementary, supplementary, vertical, adjacent, and parallel-line angles, as well as angle bisectors and perpendicular bisectors.

Skills covered

  • Finding complementary and supplementary angles
  • Using vertical-angle and linear-pair relationships
  • Solving angle equations
  • Identifying corresponding, alternate interior, and same-side interior angles
  • Understanding angle bisectors and perpendicular bisectors
  • Applying triangle, quadrilateral, and exterior-angle sums

How to use these practice tests

Use the total angle measures for a right angle, straight angle, triangle, and quadrilateral. For constructions, remember that a compass transfers equal distances while a straightedge draws lines through constructed points.

For more Grade 7 Math practice, return to the Grade 7 Math category.

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Grade 7 Angles and Geometric Constructions Practice Tests

A 10-question Grade 7 Math practice test on angle relationships, angle equations, parallel lines, constructions, triangles, and quadrilaterals.

Use angle-sum relationships, vertical and parallel-line properties, and compass-and-straightedge construction rules to solve each problem.

10 Questions
0/10 Questions0 %
Correct 0
Incorrect 0
Unanswered 10
1. QuestionMultiple choice

A triangle has angles 55∘55^\circ and 65∘65^\circ. What is the third angle?

Please select an answer first.

Correct answer: A

The correct answer is 60∘60^\circ.

  1. Identify the angle relationship or construction: Determine whether the problem uses complementary, supplementary, vertical, parallel-line, or construction properties.
  2. Apply the geometry rule: Triangle angles sum to 180∘180^\circ: 180∘−55∘−65∘=60∘180^\circ-55^\circ-65^\circ=60^\circ.
  3. Check the result: Verify the angle measure, equality, or construction step using the defining property.

Triangle angles sum to 180∘180^\circ: 180∘−55∘−65∘=60∘180^\circ-55^\circ-65^\circ=60^\circ.

2. QuestionMultiple choice

An isosceles triangle has two equal base angles of 40∘40^\circ. What is the vertex angle?

Please select an answer first.

Correct answer: B

The correct answer is 100∘100^\circ.

  1. Identify the angle relationship or construction: Determine whether the problem uses complementary, supplementary, vertical, parallel-line, or construction properties.
  2. Apply the geometry rule: The base angles total 80∘80^\circ. Subtract from 180: 180∘−80∘=100∘180^\circ-80^\circ=100^\circ.
  3. Check the result: Verify the angle measure, equality, or construction step using the defining property.

The base angles total 80∘80^\circ. Subtract from 180: 180∘−80∘=100∘180^\circ-80^\circ=100^\circ.

3. QuestionMultiple choice

A quadrilateral has angles 90∘90^\circ, 80∘80^\circ, 100∘100^\circ, and xx. What is xx?

Please select an answer first.

Correct answer: C

The correct answer is 90∘90^\circ.

  1. Identify the angle relationship or construction: Determine whether the problem uses complementary, supplementary, vertical, parallel-line, or construction properties.
  2. Apply the geometry rule: Quadrilateral angles sum to 360∘360^\circ: x=360∘−90∘−80∘−100∘=90∘x=360^\circ-90^\circ-80^\circ-100^\circ=90^\circ.
  3. Check the result: Verify the angle measure, equality, or construction step using the defining property.

Quadrilateral angles sum to 360∘360^\circ: x=360∘−90∘−80∘−100∘=90∘x=360^\circ-90^\circ-80^\circ-100^\circ=90^\circ.

4. QuestionMultiple choice

An exterior angle of a triangle has remote interior angles of 45∘45^\circ and 65∘65^\circ. What is the exterior angle?

Please select an answer first.

Correct answer: D

The correct answer is 110∘110^\circ.

  1. Identify the angle relationship or construction: Determine whether the problem uses complementary, supplementary, vertical, parallel-line, or construction properties.
  2. Apply the geometry rule: An exterior angle equals the sum of its remote interior angles: 45∘+65∘=110∘45^\circ+65^\circ=110^\circ.
  3. Check the result: Verify the angle measure, equality, or construction step using the defining property.

An exterior angle equals the sum of its remote interior angles: 45∘+65∘=110∘45^\circ+65^\circ=110^\circ.

5. QuestionMultiple choice

Corresponding angles measure 3x+103x+10 and 100∘100^\circ. What is xx?

Please select an answer first.

Correct answer: A

The correct answer is 3030.

  1. Identify the angle relationship or construction: Determine whether the problem uses complementary, supplementary, vertical, parallel-line, or construction properties.
  2. Apply the geometry rule: Set corresponding angles equal: 3x+10=1003x+10=100. Thus 3x=903x=90 and x=30x=30.
  3. Check the result: Verify the angle measure, equality, or construction step using the defining property.

Set corresponding angles equal: 3x+10=1003x+10=100. Thus 3x=903x=90 and x=30x=30.

6. QuestionMultiple choice

An angle bisector divides an angle measuring 96∘96^\circ. What is the measure of each part?

Please select an answer first.

Correct answer: B

The correct answer is 48∘48^\circ.

  1. Identify the angle relationship or construction: Determine whether the problem uses complementary, supplementary, vertical, parallel-line, or construction properties.
  2. Apply the geometry rule: Divide the full angle by 2: 96∘÷2=48∘96^\circ\div2=48^\circ.
  3. Check the result: Verify the angle measure, equality, or construction step using the defining property.

Divide the full angle by 2: 96∘÷2=48∘96^\circ\div2=48^\circ.

7. QuestionMultiple choice

Two perpendicular lines intersect. What is the measure of each angle formed?

Please select an answer first.

Correct answer: C

The correct answer is 90∘90^\circ.

  1. Identify the angle relationship or construction: Determine whether the problem uses complementary, supplementary, vertical, parallel-line, or construction properties.
  2. Apply the geometry rule: Perpendicular lines form four right angles, each measuring 90∘90^\circ.
  3. Check the result: Verify the angle measure, equality, or construction step using the defining property.

Perpendicular lines form four right angles, each measuring 90∘90^\circ.

8. QuestionMultiple choice

Two supplementary angles are in the ratio 1:21:2. What is the larger angle?

Please select an answer first.

Correct answer: D

The correct answer is 120∘120^\circ.

  1. Identify the angle relationship or construction: Determine whether the problem uses complementary, supplementary, vertical, parallel-line, or construction properties.
  2. Apply the geometry rule: Let the angles be xx and 2x2x. Then 3x=180∘3x=180^\circ, so the larger angle is 2x=120∘2x=120^\circ.
  3. Check the result: Verify the angle measure, equality, or construction step using the defining property.

Let the angles be xx and 2x2x. Then 3x=180∘3x=180^\circ, so the larger angle is 2x=120∘2x=120^\circ.

9. QuestionMultiple choice

A triangle has angles xx, x+20∘x+20^\circ, and x+40∘x+40^\circ. What is xx?

Please select an answer first.

Correct answer: A

The correct answer is 40∘40^\circ.

  1. Identify the angle relationship or construction: Determine whether the problem uses complementary, supplementary, vertical, parallel-line, or construction properties.
  2. Apply the geometry rule: Set the sum to 180: 3x+60∘=180∘3x+60^\circ=180^\circ. Thus x=40∘x=40^\circ.
  3. Check the result: Verify the angle measure, equality, or construction step using the defining property.

Set the sum to 180: 3x+60∘=180∘3x+60^\circ=180^\circ. Thus x=40∘x=40^\circ.

10. QuestionMultiple choice

An angle is split by an angle bisector into two angles of 37∘37^\circ. What is the original angle?

Please select an answer first.

Correct answer: B

The correct answer is 74∘74^\circ.

  1. Identify the angle relationship or construction: Determine whether the problem uses complementary, supplementary, vertical, parallel-line, or construction properties.
  2. Apply the geometry rule: The two congruent parts add: 37∘+37∘=74∘37^\circ+37^\circ=74^\circ.
  3. Check the result: Verify the angle measure, equality, or construction step using the defining property.

The two congruent parts add: 37∘+37∘=74∘37^\circ+37^\circ=74^\circ.

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Frequently asked questions about Grade 7 Angles and Geometric Constructions

What angle relationships are covered?

The page covers complementary, supplementary, vertical, adjacent, linear-pair, corresponding, alternate interior, and same-side interior angles.

What does a perpendicular bisector do?

It crosses a segment at its midpoint at a right angle, and every point on it is equidistant from the segment endpoints.

How many questions are on this page?

The page includes five mini tests with 10 questions each, for 50 Grade 7 Angles and Geometric Constructions questions in total.