if \( \angle \mathrm{A} \) and \( \angle \mathrm{B} \) are supplementary angles and \( \angle \mathrm{A} \) is seventeen times as large as \( \angle \mathrm{B} \), find the measures of \( \angle \mathrm{A} \) and \( \angle \) B . The measure of \( \angle \mathrm{B} \) is \( 10^{\circ} \). The measure of \( \angle \mathrm{A} \) is \( \square^{\circ} \).

Let's denote the measures of \( \angle A \) and \( \angle B \). Since they are supplementary, we have: \[ \angle A + \angle B = 180^\circ \] According to the problem, \( \angle A \) is seventeen times as large as \( \angle B \). Therefore, we can express \( \angle A \) in terms of \( \angle B \): \[ \angle A = 17 \angle B \] Now, substituting \( \angle A \) into the supplementary angle equation: \[ 17 \angle B + \angle B = 180^\circ \] \[ 18 \angle B = 180^\circ \] Now, dividing both sides by 18: \[ \angle B = 10^\circ \] Using the value of \( \angle B \) to find \( \angle A \): \[ \angle A = 17 \times 10^\circ = 170^\circ \] Thus, we find: The measure of \( \angle B \) is \( 10^\circ \). The measure of \( \angle A \) is \( 170^\circ \).