Problem 1
If $$m \angle 1 =32 $$ degrees, what is the $$m \angle 2 ? $$

Answer

$$
m \angle 1 + m \angle 2 = 180
\\
32 + m \angle 2 = 180
\\
m \angle 2 = 180-32
\\
m \angle 2 = 148
$$

Problem 2
$$ \angle c $$ and $$ \angle F $$ are supplementary. If $$m \angle C$$ is 25 degrees, what is the $$m \angle F$$?

Answer

$$
m \angle c + m \angle F = 180
\\
25 + m \angle F = 180
\\
m \angle F = 180-25 = 155
$$

Problem 3
If the ratio of two supplementary angles is 2:1, what is the measure of the larger angle?

Answer

First, since this is a ratio problem, we know that 2x + 1x = 180 , so now, let's first solve for x:
$$
3x = 180
\\
x = \frac{180}{3} = 60
$$
Now, the larger angle is the 2x which is 2(60) = 120 degrees
Answer: 120 degrees

Problem 4
If the ratio of two supplementary angles is 8:1, what is the measure of the smaller angle?

Answer

First, since this is a ratio problem, we know that 8x + 1x = 180 , so now, let's first solve for x:
$$
9x = 180
\\
x = \frac{180}{9} = 20
$$
Now, the smaller angle is the 1x which is 1(20) = 20 degrees
Answer: 20 degrees