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.

Question

Question content area bottom
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.