Angle & Triangle Quiz (7.G.5 & 7.G.2)
Questions and Answers
- 1.
Angles that have the same measure
- A.
Complementary angles
- B.
Obtuse angle
- C.
Adjacent angles
- D.
Congruent angles
Correct Answer
D. Congruent anglesExplanation
Congruent angles are angles that have the same measure. This means that the angles are equal in size and can be superimposed on each other. When two angles are congruent, their measures are equal, and they have the same shape and orientation. Therefore, congruent angles can be considered identical.Rate this question:
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- 2.
Angles formed by two intersecting lines, and are opposite each other
- A.
Vertical angles
- B.
Complementary angles
- C.
Supplementary angles
- D.
Adjacent angles
Correct Answer
A. Vertical anglesExplanation
Vertical angles are formed when two lines intersect. They are opposite each other and share a common vertex. These angles have equal measures and are congruent. In other words, if one angle measures x degrees, then its vertical angle will also measure x degrees. Vertical angles are important in geometry and are used to solve various problems involving angles and lines.Rate this question:
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- 3.
An angle with a measure less than 90 degrees
- A.
Straight angle
- B.
Acute angle
- C.
Obtuse angle
- D.
Right angle
Correct Answer
B. Acute angleExplanation
An acute angle is an angle that measures less than 90 degrees. It is smaller than a right angle (90 degrees) and a straight angle (180 degrees), and larger than an obtuse angle (greater than 90 degrees). In other words, an acute angle is a sharp angle that is less than a quarter turn.Rate this question:
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- 4.
Two angles whose measures add to 90 degrees
- A.
Right angle
- B.
Adjacent angles
- C.
Complementary angles
- D.
Supplementary angles
Correct Answer
C. Complementary anglesExplanation
Complementary angles are two angles whose measures add up to 90 degrees. In other words, when you add the measures of two complementary angles, the sum will always be 90 degrees.Rate this question:
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- 5.
Two angles whose measures add to 180 degrees
- A.
Congruent angles
- B.
Adjacent angles
- C.
Complementary angles
- D.
Supplementary angles
Correct Answer
D. Supplementary anglesExplanation
Supplementary angles are two angles whose measures add up to 180 degrees. This means that when the measures of two angles are added together, the sum will always be 180 degrees. Therefore, the correct answer is "supplementary angles".Rate this question:
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- 6.
A figure formed by two rays with a common endpoint
- A.
Ray
- B.
Line
- C.
Point
- D.
Angle
Correct Answer
D. AngleExplanation
An angle is a figure formed by two rays with a common endpoint. It consists of two arms, which are the rays, and a vertex, which is the common endpoint. The rays extend indefinitely in opposite directions, creating the shape of an angle.Rate this question:
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- 7.
Two angles that share a vertex and a side but no points in their interiors
- A.
Acute angle
- B.
Congruent angles
- C.
Adjacent angles
- D.
Straight angle
Correct Answer
C. Adjacent anglesExplanation
Adjacent angles are two angles that share a common vertex and a common side, but do not have any points in their interiors. In other words, they are side by side and do not overlap.Rate this question:
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- 8.
An angle with a measure of 90 degrees
- A.
Staight angle
- B.
Acute angle
- C.
Angle
- D.
Right angle
Correct Answer
D. Right angleExplanation
A right angle is a type of angle that measures exactly 90 degrees. It is formed when two lines intersect each other perpendicular to each other. The other options, such as a straight angle, acute angle, and angle, do not have a specific measure of 90 degrees. A straight angle measures 180 degrees, an acute angle measures less than 90 degrees, and an angle is a general term that can refer to any measure of degrees. Therefore, the correct answer is right angle.Rate this question:
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- 9.
An angle with a measure greater than 90 degrees and less than 180 degrees
- A.
Acute angle
- B.
Right angle
- C.
Angle
- D.
Obtuse angle
Correct Answer
D. Obtuse angleExplanation
An obtuse angle is an angle that measures greater than 90 degrees but less than 180 degrees. It is larger than a right angle, which measures exactly 90 degrees, and smaller than a straight angle, which measures exactly 180 degrees.Rate this question:
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- 10.
An angle with a measure of 180 degrees
- A.
Straight angle
- B.
Acute angle
- C.
Adjacent angles
- D.
Right angle
Correct Answer
A. Straight angleExplanation
A straight angle is formed when two rays lie on the same line and create a straight line. It measures exactly 180 degrees, making it the largest possible angle. This angle is often represented by a straight line with a small arc in the middle. It is called a straight angle because it forms a straight line.Rate this question:
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- 11.
If we know that the blue angle is 116°, what is the measure of angle x?
Correct Answer
116
116°
116 degreesExplanation
The measure of angle x is 116 degrees because the given information states that the blue angle is 116 degrees, and angle x is the same as the blue angle.Rate this question:
- 12.
If \angle QPS<QPS is a right angle and m<QPR = 48°, what is m<RPS?
Correct Answer
42
42°
42 degreesExplanation
Since angle QPS is a right angle, it measures 90 degrees. Given that angle QPR measures 48 degrees, we can subtract this from 90 degrees to find angle RPS. Therefore, angle RPS measures 42 degrees.Rate this question:
- 13.
If m<LON = 180° and m<MON = 133°, what is m<LOM?
Correct Answer
47
47°
47 degreesExplanation
The measure of angle LOM can be determined by subtracting the measure of angle MON from the measure of angle LON. Given that mRate this question:
- 14.
If <QPS is a right angle and m<RPS = 16°, what is m<QPR?
Correct Answer
74
74°
74 degreesExplanation
The question states that angle QPS is a right angle and angle RPS measures 16 degrees. Since angle QPS is a right angle, it measures 90 degrees. Therefore, angle QPR is the difference between angle QPS and angle RPS, which is 90 - 16 = 74 degrees.Rate this question:
- 15.
If we know that the blue angle is 99°, what is the measure of angle x?
Correct Answer
99
99°
99 degreesExplanation
The measure of angle x is 99 degrees because it is stated in the question that the blue angle is 99 degrees, and angle x is the same as the blue angle.Rate this question:
- 16.
Which set of lengths can form exactly one triangle? (Use scratch paper to draw it if you would like.)
- A.
16 feet, 8 feet, 4 feet
- B.
16 feet, 10 feet, 4 feet
- C.
16 feet, 12 feet, 4 feet
- D.
16 feet, 14 feet, 4 feet
- E.
None of the above
Correct Answer
D. 16 feet, 14 feet, 4 feetExplanation
In order for a set of lengths to form a triangle, the sum of the lengths of any two sides must be greater than the length of the third side. If we add the lengths of the sides in each set, we can see that only the set 16 feet, 14 feet, 4 feet satisfies this condition. Therefore, this set can form exactly one triangle.Rate this question:
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- 17.
Which set of lengths can form exactly one triangle? (Use scratch paper to draw it if you would like.)
- A.
6 inches, 8 inches, 2 inches
- B.
6 inches, 16 inches, 5 inches
- C.
7 inches, 14 inches, 7 inches
- D.
19 inches, 14 inches, 4 inches
- E.
None of the above
Correct Answer
E. None of the aboveExplanation
According to the triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In the given options, none of the sets of lengths satisfy this condition. For example, in the first option, the sum of the lengths of the two shorter sides (6 inches and 2 inches) is less than the length of the longest side (8 inches), violating the triangle inequality theorem. Therefore, none of the given sets of lengths can form exactly one triangle.Rate this question:
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- 18.
Which set of angles will form exactly one triangle? (You may use scratch paper to draw it if you would like)
- A.
90°, 50°, 40°
- B.
30°, 100°, 50°
- C.
100°, 80°, 20°
- D.
45°, 45°, 45°
- E.
None of the above
Correct Answer
E. None of the aboveExplanation
None of the given sets of angles will form exactly one triangle. In order to form a triangle, the sum of the measures of any two angles must be greater than the measure of the third angle. However, in the given sets of angles, this condition is not satisfied. For example, in the set of angles 90°, 50°, 40°, the sum of the measures of the two smaller angles (50° + 40° = 90°) is equal to the measure of the largest angle (90°), which means that the angles cannot form a triangle. The same reasoning can be applied to the other sets of angles as well.Rate this question:
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- 19.
Which set of angles will not form a triangle? (You may use scratch paper to draw it if you would like)
- A.
90°, 50°, 40°
- B.
30°, 100°, 50°
- C.
100°, 80°, 20°
- D.
45°, 45°, 90°
Correct Answer
C. 100°, 80°, 20°Explanation
The sum of the angles in a triangle is always 180 degrees. In the first three sets of angles, the sum of the angles is 180 degrees, so they can form a triangle. However, in the last set of angles, the sum is 180 degrees, so they cannot form a triangle.Rate this question:
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- 20.
There are some measurements that result in exactly two triangles.
- A.
True
- B.
False
Correct Answer
A. TrueExplanation
This statement is true because there are certain measurements, such as having three sides of different lengths, where it is possible to form exactly two triangles. In such cases, the triangle inequality theorem is satisfied, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. This allows for the formation of two distinct triangles.Rate this question:
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