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Quizzes > High School Quizzes > Mathematics

Practice Test: Which Angles are Linear Pairs?

Master angle pairs with interactive check-all quizzes.

Difficulty: Moderate
Grade: Grade 8
Study OutcomesCheat Sheet
Paper art for the Linear Pair Challenge, a geometry trivia quiz for high school students.

What defines a linear pair of angles?
They are opposite angles produced by two intersecting lines.
They are adjacent angles whose non-shared sides form a straight line and sum to 180°.
They are non-adjacent angles that add up to 360°.
They have a common vertex and adjacent sides, but their measures add up to 90°.
A linear pair consists of two adjacent angles that share a common vertex and side, with their other sides forming a straight line. This ensures their measures add up to 180°.
Which key property must two angles in a linear pair satisfy?
Their measures add up to 180°.
Their measures add up to 90°.
They are congruent.
They are complementary.
The defining property of a linear pair is that the two adjacent angles add up to 180°. This is a direct consequence of the straight line created by the non-shared sides.
In a diagram, two angles share a common side and have their other sides forming a straight line. What pair of angles does this represent?
Supplementary angles that are not adjacent.
Complementary angles.
A linear pair.
Vertical angles.
When two angles are adjacent and their non-common sides make a straight line, they form a linear pair. This configuration ensures that their angle measures add up to 180°.
Two adjacent angles measure 110° and 70° respectively. Do they form a linear pair?
No, because 110° and 70° are too high.
Yes, because 110° + 70° = 180°.
No, because only one angle needs to be 90°.
Yes, because any two adjacent angles form a linear pair.
Since the two adjacent angles add up to 180° (110° + 70° = 180°), they satisfy the condition for being a linear pair. This is a straightforward application of the linear pair property.
Which statement is true about the sides of angles in a linear pair?
They share a common side, and their non-common sides form a straight line.
They share a common side, but the other sides do not form a line.
They are always equal in measure.
They have no side in common.
A linear pair requires that the two angles share one common side while the other sides continue to form a straight line. This arrangement guarantees that the angles are supplementary.
If one angle in a linear pair is expressed as (2x + 20)° and its adjacent angle is (x + 40)°, what is the value of x?
x = 30
x = 50
x = 60
x = 40
Setting up the equation (2x + 20) + (x + 40) = 180 leads to 3x + 60 = 180. Solving this equation gives x = 40.
Two angles are a linear pair with one expressed as (3y - 15)° and the other as (2y + 5)°. What is the measure of the first angle?
90°
108°
99°
105°
First, set up the equation: (3y - 15) + (2y + 5) = 180, which simplifies to 5y - 10 = 180. Solving for y gives y = 38, and substituting back into 3y - 15 gives 99°.
Which pair of angles is definitely not a linear pair?
Two vertical angles produced by intersecting lines.
Two adjacent angles whose non-common sides form a straight line.
Two adjacent angles represented by (2x+30)° and (150-2x)°.
Two adjacent angles with a common side whose measures sum to 180°.
Vertical angles, although equal, are not adjacent because they do not share a common side. Thus, they cannot form a linear pair, which requires adjacency.
If angles A and B form a linear pair and angle A is 15° more than angle B, what are the measures of angles A and B?
Angle A = 90° and Angle B = 90°
Angle A = 85° and Angle B = 95°
Angle A = 100° and Angle B = 80°
Angle A = 97.5° and Angle B = 82.5°
Let angle B = x and angle A = x + 15. Since they form a linear pair, x + (x + 15) = 180, which gives x = 82.5 and angle A = 97.5°. This satisfies the given condition.
When two angles form a linear pair, if one angle is expressed as 2a and the other as (a + 60)°, what is the value of a?
30
60
45
40
The equation to be set up is 2a + (a + 60) = 180, which simplifies to 3a + 60 = 180. Solving for a gives a = 40.
Which algebraic equation represents the relationship between two angles forming a linear pair if one angle is (5x - 10)° and the other is (2x + 20)°?
(5x - 10) + (2x + 20) = 90
(5x - 10) - (2x + 20) = 180
(5x - 10) + (2x + 20) = 180
(2x + 20) - (5x - 10) = 90
Since the sum of the angles in a linear pair is 180°, the correct equation is (5x - 10) + (2x + 20) = 180. This represents the linear pair relationship accurately.
In a diagram, a straight line forms two adjacent angles with one labeled 120°. What is the measure of the other angle if they form a linear pair?
90°
120°
30°
60°
Since the two angles must add up to 180° in a linear pair, the other angle measures 180° - 120° = 60°. This is a direct application of the linear pair property.
If one angle in a linear pair is represented by (x + 25)° and the other is 155°, what is the value of x?
10
-5
0
5
The sum of the angles is given by (x + 25) + 155 = 180. This simplifies to x + 180 = 180, which immediately shows that x = 0.
Which statement about linear pairs is false?
The non-common sides of a linear pair form a straight line.
A linear pair must consist of adjacent angles.
Linear pairs always add up to 180°.
Every pair of angles that add to 180° is a linear pair.
While linear pairs do add up to 180° and are adjacent, it is not true that every pair of angles summing to 180° are linear pairs. They must also be adjacent with a common side to qualify.
If two angles forming a linear pair have measures of 2x° and (3x + 10)°, what is the value of x?
40
30
35
34
The equation is 2x + (3x + 10) = 180, which simplifies to 5x + 10 = 180. Solving for x gives x = 34.
In a complex figure, lines AB and CD intersect at point E, forming four angles. If one angle is expressed as (2x + 10)° and its linear pair is (3x - 20)°, what is the value of x and the measure of the (2x + 10)° angle?
x = 38; (2x + 10)° = 86°
x = 40; (2x + 10)° = 90°
x = 38; (2x + 10)° = 90°
x = 40; (2x + 10)° = 80°
Setting up the equation (2x + 10) + (3x - 20) = 180 gives 5x - 10 = 180, so x = 38. Substituting back, (2*38 + 10) results in 86°, confirming the correct values.
If angles P and Q form a linear pair and angle P is given as (4y - 15)° while angle Q is (3y + 20)°, what is the value of y and the measures of angles P and Q?
y = 25; angle P = 85° and angle Q = 95°
y = 25; angle P = 95° and angle Q = 85°
y = 30; angle P = 105° and angle Q = 110°
y = 20; angle P = 65° and angle Q = 80°
The equation (4y - 15) + (3y + 20) = 180 simplifies to 7y + 5 = 180, yielding y = 25. Substituting, angle P becomes 85° and angle Q becomes 95°, which correctly form a linear pair.
In a geometric proof requiring the demonstration of a linear pair, which of the following pieces of information is essential?
The angles share a common vertex and side, and their other sides lie along the same straight line.
The angles are complementary.
The angles are congruent.
The sum of the angles is 360°.
To prove a linear pair, it is essential to show that the angles share a vertex and one side, while their other sides form a straight line. This confirms that the angles are supplementary by definition.
Consider three angles A, B, and C sharing the same vertex such that A and B form a linear pair and B and C form a linear pair. If angle A = 50° and angle C = 70°, what conclusion can be drawn about angle B?
Angle B measures 50°.
Angle B measures 120°.
Angle B measures 70°.
The configuration is impossible because angle B would have to have two different measures.
If A and B form a linear pair, then B would be 130°, and if B and C form a linear pair, then B would be 110°. This inconsistency means such a configuration cannot exist.
In a diagram, angle X and angle Y form a linear pair, where angle X = (6z + 12)° and angle Y = (4z - 2)°. Given that another angle Z is 90° (unrelated to the linear pair), what is the value of z and the measure of angle Y?
z = 17; angle Y = 68°
z = 17; angle Y = 66°
z = 16; angle Y = 64°
z = 18; angle Y = 70°
By setting up the equation (6z + 12) + (4z - 2) = 180, we simplify to 10z + 10 = 180, which gives z = 17. Substituting into angle Y's expression yields 4(17) - 2 = 66°.
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Study Outcomes

  1. Understand the definition and properties of linear pairs and adjacent angles.
  2. Analyze diagrams to identify which angles form linear pairs.
  3. Apply knowledge of supplementary angles to calculate unknown angle measures in linear pairs.
  4. Evaluate and distinguish between valid and invalid examples of linear pairs in given problems.

Linear Pairs Quiz: Check All That Apply Cheat Sheet

  1. Definition of a Linear Pair - A linear pair is formed when two adjacent angles share a common side and their non-common sides create a straight line, summing to 180°. This basic concept is your first step to becoming an angle sleuth! Learn more on Cuemath
  2. Supplementary vs. Linear Pair - While all linear pairs are supplementary, not all supplementary angles form a linear pair because they might not be adjacent. Remember, adjacency is the secret ingredient that turns any two supplementary angles into a linear pair. Dive deeper on Cuemath
  3. Common Vertex & Opposite Rays - Linear pairs always share a vertex and one common arm, while their outer sides extend in exactly opposite directions (opposite rays). Spotting those opposite rays helps you quickly confirm a linear pair in any diagram. Check it out on SplashLearn
  4. Linear Pair Postulate - This postulate states that if two angles form a linear pair, then they are supplementary and add up to 180°. It's a handy rule you can use to write equations and solve angle puzzles in a snap! Explore more on OnlineMath4All
  5. Perpendicular Clue - When two intersecting lines form a linear pair of equal angles, those lines must be perpendicular. In other words, equal linear pair angles are your go-to clue for spotting right angles. Learn more on OnlineMath4All
  6. How to Identify - To confirm a linear pair, check that the angles share one side and that the other two sides form a straight line. Think of it like matching puzzle pieces: only the correct sides will line up perfectly. Details on Teachoo
  7. Diagram Etiquette - In figures, linear pairs are often marked by a straight line with two angles on each side, sometimes highlighted by small arcs or color codes. Spot these visual hints to speed through diagram-based problems. See examples on Math-Only-Math
  8. Why It Matters - Understanding linear pairs unlocks a world of angle relationships and intersecting-line problems, making tricky proofs feel like a breeze. Master this, and you'll tackle advanced geometry with confidence. Learn why on APlusTopper
  9. Practice Makes Perfect - Hunt for linear pairs in different shapes and diagrams to sharpen your angle-spotting skills. The more you practice, the faster you'll become at writing and solving equations based on these pairs. Practice worksheets on OnlineMath4All
  10. Key Takeaway: Adjacency Counts - Always double-check that your supplementary angles are adjacent before calling them a linear pair; adjacency is the defining feature. Keep this tip in mind to avoid common angle-mixing mix-ups! More on HowStuffWorks
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