QQuestionMathematics
QuestionMathematics
Explain vertical angle and horizontal angle and how they are calculated
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Answer
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Step 1
\text{If } \angle A \text{ and } \angle B \text{ are vertical angles, then } \angle A \cong \angle B.
A vertical angle is an angle that has the same vertex as another angle and is formed by a line that is parallel to the first line and intersects it. In other words, vertical angles are angles that share a common vertex and a common side but are on opposite sides of that common side. They are also called vertically opposite angles or co-interior angles. Vertical angles are always congruent, meaning they have the same measure.
Step 2
\text{If } \angle A \text{ and } \angle B \text{ are horizontal angles, then } m\angle A + m\angle B = 180^\circ.
A horizontal angle is an angle that is in the same plane as another angle and has its sides in the same line as the sides of the other angle, but on the opposite side of the vertex. Horizontal angles are also called supplementary angles because their measures add up to 180 degrees.
Final Answer
Vertical angles are angles that share a common vertex and a common side but are on opposite sides of that common side. They are always congruent, meaning they have the same measure. Horizontal angles are angles that are in the same plane as another angle and have its sides in the same line as the sides of the other angle, but on the opposite side of the vertex. They are also called supplementary angles because their measures add up to 180 degrees. To calculate the measure of a vertical angle, you can use the fact that vertical angles are congruent and subtract the measure of one vertical angle from 180 degrees. To calculate the measure of a horizontal angle, you can use the fact that horizontal angles are supplementary and subtract the measure of one horizontal angle from 180 degrees.
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