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Quizzes > High School Quizzes > Mathematics

Supplementary Angle Pairs Practice Quiz

Conquer check all that apply problems confidently

Difficulty: Moderate
Grade: Grade 7
Study OutcomesCheat Sheet
Colorful paper art promoting Supplementary Angle Showdown trivia for middle school geometry students.

What is the definition of supplementary angles?
Two angles that are congruent
Two angles whose sum is 90 degrees
Two angles whose sum is 180 degrees
Two angles that form a right angle
Supplementary angles are defined as two angles whose measures add up to 180 degrees. This fundamental concept is key in many geometric problems.
Which pair of angles is supplementary if one angle measures 110°?
90°
70°
60°
80°
Since supplementary angles add up to 180°, subtracting 110° from 180° yields 70°. Therefore, 110° and 70° form a supplementary pair.
If two angles are supplementary, what is the sum of their measures?
0 degrees
90 degrees
360 degrees
180 degrees
By definition, supplementary angles add up to 180 degrees. This basic fact is critical for solving related problems.
Which pair of angles does NOT form a supplementary set?
100° and 80°
120° and 70°
130° and 50°
90° and 90°
Supplementary angles must add up to 180°. While 130°+50°, 100°+80°, and 90°+90° all equal 180°, the pair 120° and 70° sum to 190°, so they are not supplementary.
If one angle of a supplementary pair measures 45°, what does the other angle measure?
45°
90°
180°
135°
Subtracting 45° from 180° gives 135°, which is the measure of the other angle. This ensures the two angles together sum to 180°.
Two angles are supplementary. If one angle is expressed as (3x + 10)° and the other as (5x - 30)°, what is the value of x?
15
25
30
20
Setting up the equation: (3x + 10) + (5x - 30) = 180 leads to 8x - 20 = 180. Solving for x gives 8x = 200, so x = 25.
If angle A and angle B are supplementary and angle A is twice angle B, what is the measure of angle A?
150°
90°
60°
120°
Let B = x; then A = 2x. Since A and B are supplementary, x + 2x = 180, so 3x = 180 and x = 60. Therefore, angle A = 2x = 120°.
Which equation correctly represents the relationship between two supplementary angles expressed as (x + 20)° and (2x - 10)°?
(x + 20) * (2x - 10) = 180
(x + 20) + (2x - 10) = 180
(x + 20) - (2x - 10) = 180
(x + 20) + (2x - 10) = 90
Supplementary angles add up to 180°. Therefore, the sum of the angles is represented by (x + 20) + (2x - 10) = 180.
In a diagram, two angles form a linear pair. Which term best describes their relationship?
Adjacent
Complementary
Vertical
Supplementary
A linear pair consists of adjacent angles that form a straight line, meaning their measures add up to 180°. This is the definition of supplementary angles.
What must be true for two angles to be considered supplementary?
Their measures add up to 180°
They form a right angle
They are congruent
Their measures add up to 90°
Supplementary angles are defined by the property that their measures sum to 180°. This basic criterion distinguishes them from other angle relationships.
An isosceles trapezoid has one pair of base angles measuring 70°. What is the measure of the adjacent base angle?
70°
120°
110°
90°
In an isosceles trapezoid, base angles adjacent to each other are supplementary. Therefore, the angle adjacent to 70° is 180° - 70° = 110°.
If two supplementary angles are in the ratio 2:3, what are their measures?
60° and 120°
72° and 108°
90° and 90°
80° and 100°
Express the angles as 2k and 3k. Since 2k + 3k = 180, it follows that 5k = 180 and k = 36. Thus, the angles are 2*36 = 72° and 3*36 = 108°.
If an angle is 15° less than its supplementary angle, what are the measures of the two angles?
75° and 90°
82.5° and 97.5°
85° and 100°
80° and 95°
Let the smaller angle be x and the larger be x + 15. Setting up the equation x + (x + 15) = 180 gives 2x = 165, so x = 82.5° and the larger angle is 97.5°. This ensures they are supplementary.
Solve for x if two supplementary angles are given by (4x + 10)° and (2x + 20)°.
30
25
35
20
By adding the expressions: (4x + 10) + (2x + 20) = 6x + 30 = 180, we solve for x: 6x = 150, so x = 25. This satisfies the condition for supplementary angles.
If the measure of one angle is 3 times the measure of its supplement minus 20, what is the measure of the angle?
50°
130°
140°
120°
Let the angle be A and its supplement be 180 - A. The equation becomes A = 3(180 - A) - 20. Solving this yields A = 130°. Verifying shows that 130° and 50° are indeed supplementary.
Two supplementary angles are expressed in terms of x. One angle is (4x + 16)° and the other is (2x + 44)°. Solve for x and determine the measures of the angles.
x = 18; angles: 88° and 80°
x = 20; angles: 96° and 84°
x = 20; angles: 90° and 90°
x = 22; angles: 104° and 88°
Adding the expressions (4x + 16) and (2x + 44) gives 6x + 60 = 180, so x = 20. Substituting back yields angles of 96° (4*20+16) and 84° (2*20+44), which correctly sum to 180°.
An angle and its linear pair are in a ratio such that one angle is three times the other. Find both angle measures.
45° and 135°
60° and 120°
30° and 150°
90° and 90°
Let the smaller angle be x and the larger be 3x, so x + 3x = 180 gives 4x = 180 and x = 45°. Therefore, the angles are 45° and 135°, satisfying the linear pair property.
Given two supplementary angles with measures expressed as 3y° and (y + 70)°, determine the measure of the larger angle.
82.5°
97.5°
105°
100°
Setting up the equation 3y + (y + 70) = 180 simplifies to 4y = 110, so y = 27.5. Evaluating both expressions gives angles of 82.5° and 97.5°; the larger of these is 97.5°.
If the measures of two supplementary angles are expressed as 2z + 20° and 4z + 10°, what is the value of z?
30
35
25
20
By adding the angles, (2z + 20) + (4z + 10) = 6z + 30 = 180. Solving for z gives 6z = 150, so z = 25, which satisfies the supplementary condition.
Which of the following angle pairs is NOT supplementary?
60° and 120°
110° and 70°
85° and 95°
45° and 45°
Supplementary angles must add up to 180°. While 85°+95°, 60°+120°, and 110°+70° each equal 180°, the pair 45° and 45° sums to only 90°. Thus, they are not supplementary.
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Study Outcomes

  1. Identify angle pairs that add up to 180°.
  2. Apply the concept of supplementary angles to solve geometry problems.
  3. Calculate the missing angle in a supplementary pair.
  4. Analyze geometric diagrams to determine supplementary relationships.
  5. Evaluate multiple-choice options to correctly select supplementary angle pairs.

Supplementary Angles Cheat Sheet

  1. Definition of Supplementary Angles - Dive into the basics: two angles are supplementary when their measures add up to exactly 180°. Think of them as best buddies teaming up to form a perfect straight line! This foundation will help you spot these angle pairs everywhere. Math is Fun
  2. Types of Supplementary Angles - Supplementary angles can be adjacent, sharing a common side and vertex, or non-adjacent, hanging out separately yet still summing to 180°. Adjacent pairs form a neat straight line, while non-adjacent ones still keep their sum game strong. Spotting both types sharpens your angle-spotting skills! Splash Learn
  3. Linear Pairs - When two adjacent angles create a straight line, they're called a linear pair and are always supplementary. If one angle is 120°, the other must be 60° to complete the 180° straight path. It's like a seesaw balance that never tips! GeeksforGeeks
  4. Finding a Supplementary Angle - To find the mystery partner of any angle, simply subtract its measure from 180°. For instance, if you have a 65° angle, its supplement is 180° − 65° = 115°. This quick trick turns you into a supplement sleuth! Math Warehouse
  5. Complementary vs. Supplementary Angles - Complementary angles add up to 90° ("C" for "Corner"), while supplementary angles sum to 180° ("S" for "Straight"). Remember: right-angle buddies vs. straight-line pals! This little mnemonic keeps your angle categories crystal clear. Math is Fun
  6. Real-Life Examples - Spot supplementary angles in everyday life: the clock hands at 8:00 form a 180° pair, and straight road intersections showcase them too. Even the angles of an open book can surprise you with a perfect half-circle effect. Keeping an eye out makes geometry way more fun! GeeksforGeeks - Real Life
  7. Properties of Supplementary Angles - If two angles are each supplementary to the same angle, they're congruent - meaning they're the same size. So, if ∠A + ∠B = 180° and ∠B + ∠C = 180°, then ∠A = ∠C. This cool property helps you prove all sorts of angle relationships! GeeksforGeeks - Properties
  8. Supplementary Angles in Triangles - The three interior angles of any triangle always add up to 180°. Once you know two angles, subtract their sum from 180° to find the third. This trick is your go‑to for triangle puzzles and test questions! Splash Learn - Triangles
  9. Supplementary Angles in Parallel Lines - When a transversal cuts across parallel lines, consecutive interior angles form supplementary pairs. They always add up to 180°, making your parallel-line proofs a breeze. Keep an eye on those interior angles! GeeksforGeeks - Parallel Lines
  10. Practice Problems - Sharpen your skills by solving fun angle puzzles: if one angle is twice its supplement, set up x + 2x = 180° to find x = 60° and 2x = 120°. Rinse and repeat with different ratios to level up your mastery. The more you practice, the faster you'll spot those perfect 180° duos! Math Warehouse - Practice
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