Question

One of the angles of a parallelogram is 75º. Find the measures of the remaining
angles of the parallelogram.​

Answer 1

Answer with Explanation:

Let the ABCD be the parallelogram.

Let us take ∠A to be 75° according to the question...

Now, ∠B is adjacent to ∠A...

We know that, sum of adjacent angles of parallelogram = 180°

Therefore,

∠B = 180 - 75°

So,

∠B = 105°

Now, ∠C is adjacent to ∠B,

So,

∠C = 180 - 105° = 75°

We can also do this by the property that opposite angles in a parallelogram are equal...

So, if ∠A was 75°

Then,

We know that,

∠C will be opposite to  ∠A in the parallelogram...

Therefore,

By this method also, ∠C = 75°

Now,

Using this property of oppsite angles are equal,

We can say that ∠D = ∠B,

It is because,

∠D is opposite to ∠B...

Therefore,

∠A = ∠C = 75°

∠B = ∠D = 105°

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Answer 2

Step-by-step explanation:

1. sum of all angles are 360 degree
2. since opposite angles are equal there are two angles with 75 degree
3. other two angles are 360-150/2

=105degree