16. The \( m \angle A \) is complementary to the \( m \& B \). The \( m \angle C \) is complementary to the \( m \angle B \). If \( m \angle A=62^{\circ} \), what is the \( m \angle B \) and the \( m \triangle C \) ?

To solve the problem, we need to use the properties of complementary angles. Two angles are complementary if the sum of their measures is \(90^\circ\). ### Step 1: Find \( m \angle B \) Given that \( m \angle A \) is complementary to \( m \angle B \), we can write the equation: \[ m \angle A + m \angle B = 90^\circ \] Substituting the value of \( m \angle A \): \[ 62^\circ + m \angle B = 90^\circ \] Now, we can solve for \( m \angle B \): \[ m \angle B = 90^\circ - 62^\circ \] Calculating this gives: \[ m \angle B = 28^\circ \] ### Step 2: Find \( m \angle C \) Next, we know that \( m \angle C \) is also complementary to \( m \angle B \). Therefore, we can write: \[ m \angle C + m \angle B = 90^\circ \] Substituting the value of \( m \angle B \): \[ m \angle C + 28^\circ = 90^\circ \] Now, we can solve for \( m \angle C \): \[ m \angle C = 90^\circ - 28^\circ \] Calculating this gives: \[ m \angle C = 62^\circ \] ### Final Answers - \( m \angle B = 28^\circ \) - \( m \angle C = 62^\circ \) Thus, the measures of the angles are: - \( m \angle B = 28^\circ \) - \( m \angle C = 62^\circ \)