Math: Middle School: Grades 6, 7 and 8 Quiz - Triangles and Angles (Answers)
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A triangle is a geometric form created by connecting three straight lines. Where each line connects or intersects you get an angle. A triangle will have three angles.
[readmore]An angle is measured in degrees (°). The degree of an angle runs between 0° and 180°.
Both triangles and angles are classified into three different types: acute, right and obtuse
TRIANGLES:
An acute triangle is a triangle where all three angles measure less than 90°.
Example: Angle A is 47°, Angle B is 39°, and Angle C is 12°
A right triangle is a triangle where at least one of the angles measures exactly 90°.
Example: Angle A is 68°, Angle B is 51°, and Angle C is 90°
An obtuse triangle is a triangle where at least one of the angles measures more than 90°.
Example: Angle A is 22°, Angle B is 138°, and Angle C is 44°
ANGLES:
An acute angle is an angle that measures less than 90°.
A right angle is an angle that measures exactly 90°.
An obtuse angle is an angle that measures more than 90°.
How to find the missing degree of an angle in a triangle is easy. You need to subtract the known from the sum of the three angles. If Angle A is 92° and Angle B is 31° what would Angle C be? You simply start with Angle A and subtract Angle B to get Angle C as follows:
92° - 31° = 61°
Angle C is 61° - correct? Well, not exactly because, remember, we are measuring the degree of an angle of a triangle. The three angles of a triangle must always be equal to a total of 180° (the sum of all three angles). So we need to first add together the known angles, here it is 92° and 31° and then we subtract that answer from the total of 180° as follows:
92° + 31° = 123°
180° - 123° = 57°
92° + 31° + 57° = 180°
Angle C = 57°
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72° + 33° = 105°
180° - 105° = 75° Angle C is 75° and because it is less than 90° it is an acute angle. Answer (d) is the correct answer |
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49° + 27° = 76°
180° - 76° = 104° Angle C is 104° and because it is greater than 90° it is an obtuse. Answer (a) is the correct answer |
When at least one angle is more than 90°, it is an obtuse triangle. Answer (b) is correct
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When at least one angle measures exactly 90°, it is a right triangle. Answer (a) is correct
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60° + 45° = 105°
180° - 105° = 75° Angle C is 75° and because it is less than 90° it makes it an acute angle. Answer (c) is the correct answer |
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33° + 17° = 50°
180° - 50° = 130° Angle C is 130° so Answer (d) is the correct answer |
68° + 22° = 90°
180° - 90° = 90° Angle C is 90° making it a right angle so Answer (b) is the correct answer |
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When all three angles are less than 90°, it is an acute triangle. Answer (a) is correct
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When at least one angle is more than 90°, it is an obtuse triangle. Answer (d) is correct
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180° - 126° = 54°
67 + 59 + 54 = 180°
Angle C is 54° so Answer (b) is correct