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, so if one of the angles formed is 72°, then the other three angles will also measure 72°. This is because vertical angles are formed by the intersection of two lines, creating two pairs of opposite angles that have the same measure. Therefore, the measures of the other three angles are all 72°.
Vertical angles are formed when two lines intersect. These angles are located opposite to each other and have equal measures. Therefore, if one of the vertical angles formed is 72°, the other vertical angle will also measure 72°. This is because vertical angles are always congruent.
Now, since the sum of the measures of the angles in a straight line is 180°, the sum of the two vertical angles will be 180°. So, if one of the vertical angles is 72°, the sum of the other vertical angle and 72° should be equal to 180°.
Let's represent the measure of the other vertical angle as x.
72° + x = 180°
Now, to solve for x, we can subtract 72° from both sides of the equation:
x = 180° - 72°
x = 108°
Therefore, the measures of the other three angles are 72°, 72°, and 108°.