supplementary angles
Supplementary angles are a pair of angles whose measures add up to 180 degrees
Supplementary angles are a pair of angles whose measures add up to 180 degrees. In other words, when two angles are supplementary, they combine to form a straight line.
To understand this concept further, let’s consider two angles, angle A and angle B.
If angle A measures x degrees, and angle B is supplementary to angle A, then angle B measures 180 degrees – x degrees.
For example, let’s say angle A measures 60 degrees. In this case, angle B would measure 180 degrees – 60 degrees = 120 degrees.
It’s important to note that supplementary angles do not have to be adjacent or next to each other. They could be separated by other angles or even be on different lines or planes.
Supplementary angles have several notable properties:
1. If two angles are each supplementary to a third angle, then they are congruent to each other. For example, if angle A is supplementary to angle C, and angle B is also supplementary to angle C, then angle A is congruent to angle B.
2. The sum of the interior angles of any triangle is always 180 degrees. Hence, the angles of a triangle can be considered as supplementary to each other.
3. When two parallel lines are intersected by a transversal, the alternate interior angles, corresponding angles, and consecutive interior angles are all supplementary.
4. In a quadrilateral, the sum of the measures of all interior angles is always 360 degrees. Hence, pairs of opposite angles in a quadrilateral are supplementary.
These properties can be useful when solving various geometric problems involving angles.
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