Note: Your teacher will grade your response to ensure you receive proper credit for your answer.
Two straight lengths of wire are placed on the ground, forming vertical angles. If the measure of one of the angles formed is 72°, what are the measures of the other three angles? Explain your answer.
(3 points)
Vertical angles are a pair of congruent angles formed by intersecting lines. In this case, the two straight lengths of wire form vertical angles, so the measure of one angle is 72°.
By the vertical angles theorem, the other angle opposite the 72° angle will also measure 72°. This is because vertical angles are congruent.
The sum of the measures of the angles in a straight line is 180°. Since the two angles are vertical angles, they form a straight line and their sum is 180°.
Therefore, the measure of the remaining two angles can be found by subtracting 72° from 180°.
The measure of one of the remaining angles is 180° - 72° = 108°.
Since the sum of all angles in a triangle is 180°, the measure of the final angle can be found by subtracting 72° and 108° from 180°.
The measure of the final angle is 180° - 72° - 108° = 0°.
Therefore, the measures of the other three angles are 72°, 108°, and 0°.