Angles on a Straight Line

Study Notes

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.

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.

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.

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.

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.

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.

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 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.

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.

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).