Question

8.
(i) If one of the angles of a parallelogram measures 75°, find the other angles.​

Answer 1

Answer:

75 degrees, 105 degrees and 105 degrees

Step-by-step explanation:

Here is a parallelogram.

In a parallelogram, opposite angles are congruent (the same value). As pictured the angles diagonal of each other are the same value.

Additionally, angle A and angle B must add up to be 180 degrees.



So here is a parallelogram that we can use to solve the problem.



So let’s set angle A as our given value.

angle A= 75 degrees

So therefore, angle C = 75 degrees because we know that opposite angles are congruent.

Then, we make an equation to find angle B.

Angle A + Angle B = 180 degrees

We know this because of the properties of a parallelogram.

So, plug and chug.

75 degrees + angle B = 180 degrees

(subtract 75 from both sides)

angle B = 105 degrees

And we also know that angle D = 105 degrees because opposite angles are congruent.

So, the measurements of the other angles are 75 degrees, 105 degrees and 105 degrees.