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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.
Vertical angles are pairs of angles that are opposite each other when two lines intersect. They have equal measures.
In this case, if one of the vertical angles measures 72°, then the other vertical angle will also measure 72°. This is because vertical angles are always congruent or equal.
The sum of the measures of the two vertical angles is always 180°. Therefore, the sum of 72° and 72° is equal to 144°.
To find the measures of the other two angles, we need to find the supplements of the vertical angles. The supplements of two angles are the angles that, when added together, equal 180°.
The supplement of a 72° angle can be found by subtracting 72° from 180°: 180° - 72° = 108°.
Therefore, the measures of the other two angles are 108° and 108°.