Question

If angle A and angle B are supplementary angles and angle A is nineteen times as large as angle ​B, find the measures of angle A and angle B.
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Part 1
The measure of angle B is
  
9degrees.
Part 2
The measure of angle A is
  
enter your response heredegrees.

Answer 1

Given that angles A and B are supplementary means that their measures add up to 180 degrees. According to the information provided:

- Let the measure of angle B be \( x \).
- Then the measure of angle A is \( 19x \).

Since they are supplementary, we can write the equation:

\[
x + 19x = 180
\]

Combining the terms gives:

\[
20x = 180
\]

Now, solve for \( x \):

\[
x = \frac{180}{20} = 9
\]

This means that the measure of angle B is \( 9 \) degrees.

Now, we can find the measure of angle A:

\[
\text{Angle A} = 19x = 19 \times 9 = 171 \text{ degrees}
\]

So, the results are:

- The measure of angle B is **9 degrees**.
- The measure of angle A is **171 degrees**.