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Questions and Answers
What is the sum of angles on a straight line?
If two angles on a straight line are 40 degrees and X, what is the value of X?
If a straight line has an acute angle of 25 degrees and an obtuse angle X, what is the value of X?
If a straight line has three angles: 60 degrees, X, and 30 degrees, what is the value of X?
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If a straight line has a right angle (90 degrees) and an angle of 48 degrees, what is the value of the third angle X?
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If two angles are 105 degrees and 75 degrees, are they on a straight line?
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Study Notes
Angles on a Straight Line
- Angles on a straight line add up to 180 degrees.
- If two angles on a straight line are known, the third angle can be found by subtracting the sum of the two angles from 180 degrees.
- Example: If one angle is 30 degrees (acute) and the other angle is X (obtuse), X can be found by subtracting 30 from 180 degrees, resulting in X = 150 degrees.
Example 1
- Given a straight line with an acute angle of 30 degrees and an obtuse angle X, find the size of X.
- Solution: 180 - 30 = X, so X = 150 degrees.
Example 2
- Given a straight line with an obtuse angle of 117 degrees and an angle X, find the size of X.
- Solution: 180 - 117 = X, so X = 63 degrees.
Example 3
- Given a straight line with three angles: 58 degrees, X, and 43 degrees, find the size of X.
- Solution: Add 58 and 43 to get 101, then subtract 101 from 180 to find X, resulting in X = 79 degrees.
Example 4
- Given a straight line with a right angle (90 degrees), an angle of 38 degrees, and an angle X, find the size of X.
- Solution: Add 38 and 90 to get 128, then subtract 128 from 180 to find X, resulting in X = 52 degrees.
Example 5
- Given a straight line with two angles, one of which is 65 degrees, find the size of the unknown angle X.
- Solution: Subtract 65 from 180 to find X, resulting in X = 115 degrees.
Example 6
- Given two angles, 95 degrees and 83 degrees, determine if they are on a straight line.
- Solution: Add 95 and 83 to get 178, which is not equal to 180, so the angles are not on a straight line.
Angles on a Straight Line
- Angles on a straight line always add up to 180 degrees.
- If two angles on a straight line are known, the third angle can be found by subtracting the sum of the two angles from 180 degrees.
Finding Unknown Angles
- To find an unknown angle, subtract the known angles from 180 degrees.
- If one angle is acute (less than 90 degrees) and the other is obtuse (greater than 90 degrees), subtract the acute angle from 180 to find the obtuse angle.
- If two angles are given, subtract their sum from 180 to find the unknown angle.
Examples and Applications
- If an acute angle is 30 degrees and an obtuse angle X is unknown, X = 180 - 30 = 150 degrees.
- If an obtuse angle is 117 degrees and an angle X is unknown, X = 180 - 117 = 63 degrees.
- If three angles are on a straight line, the sum of two known angles can be subtracted from 180 to find the unknown angle.
- A right angle (90 degrees) can be used as a reference point to find unknown angles.
- If two angles are given, their sum can be checked to determine if they are on a straight line (sum should be 180 degrees).
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Description
This quiz covers how to find unknown angles on a straight line by applying the concept that angles on a straight line add up to 180 degrees. Example problems are also included.
