The sum of angles 2 and 4 is 68.
Understanding Supplementary Angles:
Imagine two straight lines intersecting each other. The four angles formed where the lines meet add up to 180 degrees.
Image of two intersecting lines with labeled angles 1, 2, 3, and 4, where angles 1 and 2 are supplementary and angles 3 and 4.
In your case, angle 1 measures 146 degrees, and angles 1 and 2 form a straight line. Therefore, angle 2 must be the difference between 180 degrees and angle 1. This is because the sum of supplementary angles must be 180 degrees.
2. Calculating Angle 2:
As you correctly stated, 180 degrees - 146 degrees = 34 degrees.
Therefore, angle 2 measures 34 degrees.
3. Identifying Vertical Angles:
Now, let's look at angles 2 and 4. They are positioned opposite each other on the intersecting lines. These types of angles are called vertical angles.
4. The Property of Vertical Angles:
An important property of vertical angles is that they are congruent, meaning they have the same measure. This is because the intersecting lines create a "flip" symmetry, making the angles mirror images of each other.
5. Calculating the Sum of Angles 2 and 4:
Since angle 2 is 34 degrees and it's congruent to angle 4, then angle 4 also measures 34 degrees.
Finally, to find the sum of angles 2 and 4, we simply add them: 34 degrees + 34 degrees = 68 degrees.
Therefore, the sum of angles 2 and 4 is 68 degrees.