One of the angles of a parallelogram is 75º. Find the measures of the remaining
angles of the parallelogram.
Answers
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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Step-by-step explanation:
- sum of all angles are 360 degree
- since opposite angles are equal there are two angles with 75 degree
- other two angles are 360-150/2
=105degree