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 always congruent, which means that they have the same measure. Therefore, if one of the angles formed is 72°, the measure of the other vertical angle is also 72°.
Additionally, vertical angles are formed when two lines intersect, and they are always opposite each other. This means that the other two angles formed from the intersection of the two straight lengths of wire will also be congruent to each other.
So, the measures of the other three angles are all 72°.
Vertical angles are formed when two lines intersect. They are opposite each other and have equal measures. In this case, we have two straight lengths of wire forming vertical angles.
Given that one of the angles formed is 72°, we know that its vertical angle will also measure 72°. Therefore, we have two angles with measures of 72° each.
Since the sum of the measures of vertically opposite angles is always 180°, we can find the measures of the other two angles by subtracting the sum of the measures of the known angles from 180°.
Let's calculate:
For the two angles with measures of 72° each, the sum of their measures is 72° + 72° = 144°.
To find the measure of the first unknown angle, we subtract the sum of the known angles from 180°:
180° - 144° = 36°
Therefore, the first unknown angle measures 36°.
To find the measure of the second unknown angle, we also subtract the sum of the known angles from 180°:
180° - 144° = 36°
Therefore, the second unknown angle also measures 36°.
In summary, the measures of the four angles formed are: 72°, 72°, 36°, and 36°.