Two lines intersect at a point. The vertical angles formed are supplementary. What is the measure of each of the angles?
So my question is if both angle 1 and 2 must equal 90 degrees each?
Im wondering because I know that angle 1 and angle 2 has to equal 180, but I'm second guessing whether or not they both have to be 90 degrees! Like one can be 80 degrees while the other is 100, for example.
Vertical angles are always equal.
If they are also supplementary, they must both be 90°
The measures are 90 degrees. The reason is that vertical angles are both the same number of degrees and supplementary angles measure up to 180. So it can not be 80 and 100 because they are both not the same number of degrees. That is why 90 degrees is the only logical option.
Oh okay. Thank you for clarifying!
Well, let me enlighten you with a little clown wisdom! When two lines intersect, the vertical angles formed are always congruent, meaning they have the exact same measure. And in this case, if the vertical angles are supplementary, that means their measures add up to 180 degrees. So regardless of their individual measures, they must both have the same value. It's like a synchronized dance of angles! So each angle would have a measure of 90 degrees. Keep your angles dancing harmoniously!
The measure of each angle formed by two intersecting lines depends on the relationship between the angles. In the given scenario, if the vertical angles formed are supplementary, it means that they add up to a total of 180 degrees. However, it doesn't necessarily mean that each angle is 90 degrees.
Vertical angles are formed when two lines intersect. They are opposite to each other and have the same measure. So, if both angles are equal, you can assume that each angle measures x degrees. Since the vertical angles are supplementary, the sum of the measures of the two vertical angles is 180 degrees.
Therefore, you can set up the equation:
x + x = 180
Simplifying the equation:
2x = 180
To find x, divide both sides of the equation by 2:
x = 180/2
x = 90
So, in this case, each angle measures 90 degrees. However, it is important to note that it is not necessary for both angles to be 90 degrees. As long as their sum is 180, they can have different measures. For example, one angle could measure 80 degrees, and the other angle could measure 100 degrees.