Math K-Plus

Supplementary Angles

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What Are Supplementary Angles?


When two angles add up to 180 degrees they are called Supplementary Angles. For an example, closely look at the diagram below. We have a straight line which is a 180° angle. This 180° angle is cut in two by ray EF. So now the 180° is divided in to two smaller angles that add up to 180°. Now let us express this definition in geometric math terms. Supplementary angles in geometry have the following characteristics.
  • First let's start with a Straight Angle: ∠DEC. We already know that Straight Angle are 180°.
  • Now let us draw a Ray EF. The angle at ∠FEC is 33°.
  • If we look at the diagram below, the two adjacent angles are ∠DEF and d∠FEC. The sum of these two angles are 180° because they form a Straight Angle.
  • We know 180° minus ∠FEC equals ∠DEF. ∠FEC equals 33°. So 180° minus 33° equals 147°. So the angle at ∠DEF equals 147°.
Supplementary Angles