Question 5

We will use the properties of a parallelogram to find the unknown angles.

Step 1 — Find angle D

In a parallelogram, opposite angles are equal. Angle D is opposite to angle B. We are given that $\angle B = \mathbf{80^\circ}$.

$\angle D = \angle B$

$\boxed{\angle D = 80^\circ}$

Step 2 — Find angle A

In a parallelogram, consecutive angles are supplementary. This means they add up to $\mathbf{180^\circ}$. Angle A and angle B are consecutive angles.

$\angle A + \angle B = 180^\circ$

$\angle A + 80^\circ = 180^\circ$

$\angle A = 180^\circ - 80^\circ$

$\boxed{\angle A = 100^\circ}$

Step 3 — Find angle C

In a parallelogram, opposite angles are equal. Angle C is opposite to angle A. We found that $\angle A = \mathbf{100^\circ}$.

$\angle C = \angle A$

$\boxed{\angle C = 100^\circ}$

Answer

(i) $\angle D = 80^\circ$ (ii) $\angle A = 100^\circ$ (iii) $\angle C = 100^\circ$