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 figure is a parallelogram abcd with ∠a = 79°)

Explanation:

Step1: Use consecutive angles property

In a parallelogram, consecutive angles are supplementary (sum to $180^\circ$). For $\angle A$ and $\angle B$:
$m\angle B = 180^\circ - m\angle A = 180^\circ - 79^\circ$

Step2: Calculate $m\angle B$

$m\angle B = 101^\circ$

Step3: Use opposite angles property

In a parallelogram, opposite angles are equal. $\angle C$ is opposite $\angle A$:
$m\angle C = m\angle A = 79^\circ$

Step4: Use opposite angles property

$\angle D$ is opposite $\angle B$:
$m\angle D = m\angle B = 101^\circ$

Answer:

$m\angle B = 101^\circ$
$m\angle C = 79^\circ$
$m\angle D = 101^\circ$