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

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Part 1
The measure of angle B is
  
enter your response heredegrees.

Answer 1

Let the measure of angle B be \( x \) degrees. Since angle A is nineteen times as large as angle B, we can express angle A as \( 19x \).

Since angles A and B are supplementary, the sum of their measures is 180 degrees. We can write the equation:

\[ x + 19x = 180 \]

Combining like terms, we have:

\[ 20x = 180 \]

Now, we can solve for \( x \):

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

Thus, the measure of angle B is \( 9 \) degrees.

Now, to find the measure of angle A:

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

Final answer: The measure of angle B is \( 9 \) degrees.