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 \( \square^{\circ} \).

Let's denote \( \angle A \) as \( 17x \) and \( \angle B \) as \( x \), given that \( \angle A \) is seventeen times \( \angle B \). Since they are supplementary, we can write the equation: \[ \angle A + \angle B = 180^\circ \] Substituting the expressions for \( \angle A \) and \( \angle B \): \[ 17x + x = 180^\circ \] This simplifies to: \[ 18x = 180^\circ \] Now, divide both sides by 18: \[ x = 10^\circ \] So, \( \angle B = 10^\circ \). Now we can find \( \angle A \): \[ \angle A = 17 \times 10^\circ = 170^\circ \] Thus, the measures of \( \angle A \) and \( \angle B \) are \( 170^\circ \) and \( 10^\circ \) respectively. The measure of \( \angle B \) is \( 10^\circ \).