<2 = 39°. Find m<4 and explain how you know. Drawing not to scale.
To find the measure of angle 4, we need to use the information that angle 2 measures 39 degrees. However, we would also need additional information such as the relationship between angle 2 and angle 4, or any other angles in the diagram.
Unfortunately, based on the given information alone, it is not possible to determine the measure of angle 4.
To find the measure of angle 4, we need to use the fact that the sum of the measures of the angles in a triangle is 180 degrees.
First, let's label the angles in the given diagram:
1
_______/____________
/ \
2/ \3
-----------------------------------
4
We know that angle 2 is less than angle 39 degrees. So, angle 2 is less than 39 degrees.
Since angle 2 and angle 3 are adjacent angles that share a side, we can say that the sum of angle 2 and angle 3 equals angle 4.
So, angle 4 = angle 2 + angle 3
Since angle 2 is less than 39 degrees, and angle 3 (which is angle 2 + 1) is 39 degrees, we can substitute the values to find angle 4:
angle 4 = angle 2 + angle 3
= <2 + <3
= 39° + <2 (since <2 < 39°)
Therefore, m<4 = 39° + <2 (where <2 is the measure of angle 2).