Question

1 find the missing angle measures of the parallelogram.
m∠b=_________
m∠c=_________
m∠d=_________

Explanation:

Step1: Recall properties of parallelograms

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

Step2: Find \( m\angle B \)

Given \( m\angle A = 98^\circ \), since \( \angle A \) and \( \angle B \) are consecutive angles in a parallelogram, \( m\angle A + m\angle B=180^\circ \). So \( m\angle B = 180^\circ - 98^\circ = 82^\circ \).

Step3: Find \( m\angle C \)

By the property of parallelograms (opposite angles are equal), \( \angle A=\angle C \). Since \( m\angle A = 98^\circ \), then \( m\angle C = 98^\circ \).

Step4: Find \( m\angle D \)

By the property of parallelograms (opposite angles are equal), \( \angle B=\angle D \). Since \( m\angle B = 82^\circ \), then \( m\angle D = 82^\circ \).

Answer:

\( m\angle B = 82^\circ \), \( m\angle C = 98^\circ \), \( m\angle D = 82^\circ \)