Find all the angles of a parallelogram if one angle is 80°.
Answers
Answer:
angle A= 80°
angle C = angle A ( opposite angles of a parallelogram are equal)
so angle C= 80°
angle A + angle D = 180° ( sum of adjacent angles of a parallelogram is 180° )
80°+ angle D = 180°
angle D= 180-80
angleD = 100°
angle D = angle B
therefore angle B = 100°
hope it helps..
QuestioN :
Find all the angles of a parallelogram if one angle is 80°.
GiveN :
- One angle = 80°.
To FiNd :
- Find all the angles of a parallelogram.
ANswer :
The angles of a parallelogram are:
∠A = 80°
∠B = 100°
∠C = 80°
∠D = 100°
SolutioN :
For a parallelogram ABCD, opposite angles are equal.
So, the angles opposite to the given 80° angle will also be 80°.
It is also known that the sum of angles of any quadrilateral = 360°.
So, if ∠A = ∠C = 80° then,
∠A + ∠B + ∠C + ∠D = 360°
Also, ∠B = ∠D
Thus,
80° + ∠B + 80° + ∠D = 360°
Or, ∠B +∠ D = 200°
Hence, ∠B = ∠D = 100°
Now, all angles of the quadrilateral are found which are:
∠A = 80°
∠B = 100°
∠C = 80°
∠D = 100°
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