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Quizzes > High School Quizzes > Mathematics

Practice Quiz: Angle Relationships

Test Your Angle Knowledge With Practice Problems

Difficulty: Moderate
Grade: Grade 7
Study OutcomesCheat Sheet
Paper art depicting a trivia quiz on geometry for high school students.

Which pair of angles is defined as two angles whose measures add up to 90°?
Complementary angles
Vertical angles
Supplementary angles
Adjacent angles
Complementary angles add up to 90°. The other options do not have this property.
When two lines intersect, the non‑adjacent angles that are opposite each other are known as:
Adjacent angles
Linear pairs
Vertical angles
Complementary angles
Vertical angles are the non‑adjacent angles formed when two lines intersect, and they are congruent. The other options describe different angle relationships.
What is the measure of a right angle?
90°
180°
45°
360°
A right angle is defined as exactly 90°. The other measures represent different types of angles or full rotations.
Two angles that have a sum of 180° are called:
Complementary angles
Vertical angles
Supplementary angles
Acute angles
Supplementary angles are defined as two angles that add up to 180°. The other terms refer to different angle relationships.
What do we call angles that share a common arm and have a common vertex without overlapping?
Vertical angles
Adjacent angles
Complementary angles
Supplementary angles
Adjacent angles share a common vertex and a common side, making them next to each other but not overlapping. This distinguishes them from other angle relationships.
If one angle is 30° and it is complementary to another angle, what is the measure of the other angle?
90°
120°
60°
30°
Complementary angles have a sum of 90°. Subtracting 30° from 90° gives 60° as the measure of the second angle.
If one angle measures 110° and it is supplementary to another, what is the measure of the unknown angle?
70°
90°
100°
110°
Supplementary angles add up to 180°. Subtracting 110° from 180° results in 70°, which is the measure of the unknown angle.
What is the sum of the interior angles in a triangle?
90°
270°
360°
180°
A fundamental property of triangles is that the interior angles add up to 180°. This theorem is used in many geometric proofs and problems.
In a triangle, if two angles measure 40° and 50°, what is the measure of the third angle?
100°
80°
70°
90°
The sum of the interior angles of a triangle is 180°. Subtracting the sum of 40° and 50° (which is 90°) from 180° leaves 90° for the third angle.
When two parallel lines are cut by a transversal, which pair of angles are always supplementary?
Consecutive interior angles
Alternate interior angles
Vertical angles
Corresponding angles
Consecutive interior angles (or same‑side interior angles) are always supplementary when two parallel lines are intersected by a transversal. The other pairs have different relationships.
If two interior angles on the same side of a transversal measure 65° and 85°, are the lines parallel?
Yes
No
They are perpendicular
Cannot be determined
For lines to be parallel, consecutive interior angles must add up to 180°. Since 65° + 85° equals 150°, the lines are not parallel.
What is an exterior angle of a triangle equal to?
The sum of the two adjacent interior angles
The sum of the two non‑adjacent interior angles
The difference of the two non‑adjacent interior angles
Half of the interior angles
According to the exterior angle theorem, an exterior angle of a triangle equals the sum of the two remote (non‑adjacent) interior angles. This is a key concept in triangle geometry.
Find the value of x if two supplementary angles are given by 2x and (x + 30).
50
45
60
40
Setting up the equation for supplementary angles gives 2x + (x + 30) = 180. Simplifying to 3x + 30 = 180, we find that x = 50.
In a diagram, two angles are represented by the expressions 3x and 2x. If these angles are complementary, what is the value of x?
15
20
10
18
Complementary angles add up to 90°. So, setting up the equation 3x + 2x = 90 leads to 5x = 90, which implies x = 18.
If an angle of 120° is adjacent to another angle forming a linear pair, what is the measure of the adjacent angle?
30°
90°
120°
60°
A linear pair of angles sums to 180°. Subtracting 120° from 180° gives the adjacent angle as 60°.
Angles around a point always sum to what total measure?
360°
270°
180°
90°
All angles around a point add up to 360°. This fundamental result is used frequently in geometric problems.
In a configuration where two lines intersect, one angle is expressed as (2x + 10) and its vertical angle is 140°. What is the value of x?
65
60
55
70
Vertical angles are congruent. Therefore, setting 2x + 10 equal to 140 and solving yields x = 65.
A quadrilateral has interior angles of (x), (2x - 10), (3x + 20), and (4x - 30). What is the value of x?
40
36
38
42
The sum of the interior angles in any quadrilateral is 360°. Adding the expressions gives 10x - 20 = 360, so solving for x results in x = 38.
Two parallel lines are cut by a transversal. If one of the corresponding angles is expressed as (3x - 15)° and its corresponding angle is 75°, what is the value of x?
25
35
30
45
Because corresponding angles are congruent when lines are parallel, setting 3x - 15 equal to 75 gives the equation 3x = 90, which means x = 30.
In a diagram, three angles are arranged such that the first is (x)°, the second is (2x)°, and the third is (3x)°. If they form a straight line, what is the value of x?
20°
40°
25°
30°
Angles on a straight line total 180°. Since x + 2x + 3x equals 6x, solving 6x = 180° results in x = 30°.
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Study Outcomes

  1. Analyze various angle relationships, including complementary, supplementary, and vertical angles.
  2. Apply angle properties to solve geometric problems and identify unknown measures.
  3. Interpret geometric diagrams to accurately determine angle types and relationships.
  4. Synthesize problem-solving strategies that reinforce accurate calculation of angle measures.
  5. Evaluate one's understanding of angle concepts to build confidence for high-stakes tests or exams.

Angle Relationships Cheat Sheet

  1. Complementary Angles - These angles team up to sum to exactly 90°, like a perfect elbow turn. If you spot a 30° angle, its complement must be 60° to complete the right angle duo. education.com worksheet
  2. Supplementary Angles - Supplementary angles pair up to make a straight line, totaling 180°. Spot a 110° angle? Its partner is 70° to form that smooth line. education.com worksheet
  3. Vertical Angles - When two lines cross, they create opposite angles that are mirror images in measure. If one measures 45°, the angle right across from it is also 45°. education.com worksheet
  4. Adjacent Angles - These angles share a common side and vertex but don't overlap, like neighbors next door. Depending on their measures, they can be complementary, supplementary, or neither. education.com worksheet
  5. Linear Pair - A linear pair is a special case of adjacent angles whose non‑shared sides form a straight line, so they always add to 180°. Think of them as best buddies making a perfect half‑circle. education.com worksheet
  6. Alternate Interior Angles - Cross a transversal over two parallel lines, and look inside for angles on opposite sides of the transversal; they're congruent. These are your secret weapon for proving lines are parallel. Fiveable angle relationships
  7. Alternate Exterior Angles - Similar to their interior cousins, these angles form outside the parallel lines on opposite sides of the transversal and remain congruent. They're like matching twins on the sidewalk outside the lines. Fiveable angle relationships
  8. Corresponding Angles - When a transversal cuts across parallel lines, corresponding angles sit in the same relative corner at each intersection and share the same measure. It's like copy‑and‑paste for angles. Fiveable angle relationships
  9. Same‑Side Interior Angles - Also called consecutive interior angles, these sit on the same side of the transversal inside the parallels and together add up to 180°. They're the dynamic duo of interior angle pairs. Fiveable angle relationships
  10. Exterior Angle Theorem - In any triangle, an exterior angle equals the sum of the two non‑adjacent interior angles. This theorem is a quick trick to chase down missing angles in triangles. Wikipedia: Exterior Angle Theorem
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