The given angles in the parallelogram are ∠1 = 75°, ∠2 = 180°, ∠3 = 75°, and ∠4 = 180°, satisfying the properties of opposite angles equality and consecutive angles adding up to 180°.
∠1 = 75° (given)
Using the property that opposite angles are equal:
∠3 = ∠1 = 75°
Now, for consecutive angles:
∠2 = ∠1 + 180° - ∠3
= 75° + 180° - 75°
= 180° (since opposite angles are equal)
So far, we have:
∠1 = 75°
∠2 = 180°
∠3 = 75°
Now, for ∠4, which is also a consecutive angle with ∠2:
∠4 = ∠2
= 180° (consecutive angles add up to 180°)
Therefore, the missing angle measures are:
∠1 = 75°
∠2 = 180°
∠3 = 75°
∠4 = 180°
These angles satisfy the properties of a parallelogram, where opposite angles are equal, and consecutive angles add up to 180°.