Two straight lengths of wire are placed on the ground, forming vertical angles. If the measure of one of the angles formed is 72 degrees, what are the measures of the other three angles? Explain your angles.
Vertical angles are formed when two lines intersect. The angles that are opposite each other at the intersection are called vertical angles. These angles are congruent, which means they have the same measure.
In this case, if one of the vertical angles measures 72 degrees, the other vertical angle will also measure 72 degrees. This is because vertical angles are equal in measure.
So, the measure of the other two angles would be 72 degrees each.
Vertical angles are formed when two lines intersect. They are opposite to each other and have equal measures. In this case, the two straight lengths of wire form vertical angles.
Given that one angle measures 72 degrees, we know that its vertical angle will also measure 72 degrees. This is because vertical angles are equal.
So, the measures of the other three angles can be determined as follows:
1. The angle opposite the 72-degree angle will also measure 72 degrees. This is because vertical angles have equal measures.
2. The remaining two angles are not vertical angles, but they are adjacent angles. Adjacent angles are angles that share a common side and a common vertex but do not overlap. In this case, the two remaining angles share a common side and a common vertex, which is formed by the intersection of the two wires.
Since the sum of adjacent angles formed around a point is always 180 degrees, we can calculate the measures of the remaining two angles.
Let's denote one of the remaining angles as "x". So, the sum of the adjacent angles is:
72 degrees + 72 degrees + x = 180 degrees.
Simplifying the equation, we get:
144 degrees + x = 180 degrees.
Now, we can solve for "x" by subtracting 144 degrees from both sides of the equation:
x = 180 degrees - 144 degrees.
Simplifying further, we find:
x = 36 degrees.
Therefore, the measure of the two remaining angles is 72 degrees each, and the measure of the third angle is 36 degrees.