Two angles <3 and <5 are supplementary to <4. If m<5 is 78 degrees, what is m<3? (A diagram is required, label the diagram)

I take this to mean that each of <3 and <5 is supplementary to <4. So,

m<3 + m<4 = 180
m<5 + m<4 = 180
In that case,
78 + m<4 = 180
m<4 = 102
Now, knowing that, w can find m<3:

m<4 + 102 = 180
m<4 = 72

This makes sense, since angles supplementary to a given angle are equal.

To answer this question, we need to understand the concepts of supplementary angles and their relationship to angle <4.

Supplementary angles are two angles that add up to 180 degrees. We are given that angles <3 and <5 are supplementary to angle <4. Let's say angle <3 is x degrees, and angle <5 is 78 degrees.

Now, let's represent the given information on a diagram:

<4
_______________
| |
<3 | | <5
| |
_______________

Now, since angles <3 and <5 are supplementary to angle <4, we can write their sum as:

x + 78 degrees = 180 degrees

To find the value of x, we'll solve this equation.

Subtracting 78 from both sides of the equation, we have:

x = 180 degrees - 78 degrees
x = 102 degrees

Therefore, angle <3 measures 102 degrees.