Question

practice with parallelogram theorems.
what are the remaining angle measures if the figure is to be a parallelogram?
m∠b =
°
m∠c =
°
m∠d =
°
(the parallelogram has vertices a, b, c, d with ∠a = 79°)

Explanation:

Step1: Recall parallelogram angle properties

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

Step2: Find \(m\angle B\)

Since \(\angle A\) and \(\angle B\) are consecutive angles in a parallelogram, they are supplementary. So, \(m\angle B = 180^\circ - m\angle A\).
\(m\angle B = 180^\circ - 79^\circ = 101^\circ\)

Step3: Find \(m\angle C\)

In a parallelogram, opposite angles are equal. \(\angle A\) and \(\angle C\) are opposite, so \(m\angle C = m\angle A\).
\(m\angle C = 79^\circ\)

Step4: Find \(m\angle D\)

In a parallelogram, opposite angles are equal. \(\angle B\) and \(\angle D\) are opposite, so \(m\angle D = m\angle B\).
\(m\angle D = 101^\circ\)

Answer:

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