How to Calculate an Adjacent Angle
Adjacent angles are two angles that have a common side and vertex. The vertex is the corner point of the angle. If the sum of two adjacent angles is more or less than, but not exactly, 90 or 180 degrees, you can calculate an unknown adjacent angle if you know the other adjacent angle and the sum of the two angles. If the sum of two adjacent angles forms a right angle (exactly 90 degrees) or a straight angle (exactly 180 degrees), you can calculate one unknown adjacent angle if you know only the other adjacent angle.
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Instructions
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Using the Sum of the Two Angles
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1
Determine the known adjacent angle and known sum of the two angles. For the following example, use 80 degrees for the known adjacent angle and 150 degrees for the known sum of the two adjacent angles.
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2
Subtract the known adjacent angle from the known sum of the two angles to determine the unknown adjacent angle. In the example, subtract 80 from 150, which equals 70.
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3
Record your answer in degrees. This equals 70 degrees, which is the unknown adjacent angle.
Right Angle
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4
Determine the known adjacent angle that forms a right angle with the unknown adjacent angle. For the following example, use 62 degrees for the known adjacent angle. These two angles are called adjacent complementary angles because their sum equals 90 degrees.
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5
Subtract the known adjacent complementary angle from 90 to determine the unknown adjacent complementary angle. In the example, subtract 62 from 90, which equals 28.
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6
Record your answer in degrees. This equals 28 degrees, which is the unknown adjacent complementary angle.
Straight Angle
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7
Determine the known adjacent angle that forms a straight angle with the unknown adjacent angle. For the following example, use 120 degrees for the known adjacent angle. These two angles are called adjacent supplementary angles because their sum equals 180 degrees.
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8
Subtract the known adjacent supplementary angle from 180 to determine the unknown adjacent supplementary angle. In the example, subtract 120 from 180, which equals 60.
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9
Record your answer in degrees. This equals 60 degrees, which is the unknown adjacent supplementary angle.
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Tips & Warnings
Check your answer in each section by adding the two adjacent angles to see that you get the known sum of the two adjacent angles for that respective section.
References
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