Question

what are the remaining angle measures if the figure is to be a parallelogram? m∠b = ° m∠c = ° m∠d = ° 11 79 101 180

Explanation:

Step1: Properties of parallelogram angles

In a parallelogram, consecutive angles are supplementary (sum to \(180^{\circ}\)), and opposite angles are equal.
So, \(m\angle A + m\angle B=180^{\circ}\), \(m\angle A = m\angle C\), \(m\angle B = m\angle D\).
Given \(m\angle A = 79^{\circ}\).

Step2: Find \(m\angle B\)

Using \(m\angle A + m\angle B = 180^{\circ}\), substitute \(m\angle A = 79^{\circ}\).
\(m\angle B=180^{\circ}-79^{\circ}=101^{\circ}\).

Step3: Find \(m\angle C\)

Since \(m\angle A = m\angle C\) (opposite angles of parallelogram), \(m\angle C = 79^{\circ}\).

Step4: Find \(m\angle D\)

Since \(m\angle B = m\angle D\) (opposite angles of parallelogram), \(m\angle D = 101^{\circ}\).

Answer:

\(m\angle B = 101^{\circ}\), \(m\angle C = 79^{\circ}\), \(m\angle D = 101^{\circ}\)