Two straight lines 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 formed when two lines intersect. They are congruent, meaning they have the same measure. In this case, if one of the angles formed is 72 degrees, then the measure of the other vertical angle will also be 72 degrees. Additionally, the two remaining angles will each be supplementary to one of the vertical angles. This means that they will add up to 180 degrees. Therefore, the measures of the other three angles will be: 72 degrees, 72 degrees, and 180 degrees.
Vertical angles are always congruent, which means they have the same measure. So, if one of the angles formed by the two straight lines is 72 degrees, the measure of the other three angles will also be 72 degrees.
This is because vertical angles are formed opposite to each other when two lines intersect. They are formed by the intersection of two straight lines, and they share a common vertex but do not share a common side.
In this case, two straight lines have formed vertical angles, and the measure is given as 72 degrees for one angle. As vertical angles are congruent, the measure of the other three angles will also be 72 degrees.
To understand the measure of the other three angles formed by two straight lines, we need to consider the properties of vertical angles.
Vertical angles are always congruent, which means they have the same measure. So, if one of the angles formed is 72°, the other angle that is vertically opposite to it will also measure 72°.
Now, when two straight lines intersect, they form two pairs of vertically opposite angles. In this case, we have one pair with a measure of 72°, and we can find the measures of the other two angles with some basic geometry knowledge.
Since the sum of the measures of angles around a point is 360°, and the two angles we have already determined are 72° each, we can subtract their sum from 360° to find the total measure of the other two angles.
360° - (72° + 72°) = 360° - 144° = 216°
So, the total measure of the other two angles combined is 216°. Since they are vertically opposite angles, each angle will have a measure of half this total, which means each of the two remaining angles will measure 108°.
In summary, the measures of the other three angles formed by the two straight lines are: 72°, 72°, and 108°.