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Answers
Step-by-step explanation:
Given :-
In ABCD paralellogram , angle BDC = 30° and angle DBC = 85°
To find:-
Find all the angles of the paralellogram?
Solution:-
Method-1:-
In the Parallelogram ABCD
AB || CD and BD is a transversal then
angle BDC = angle DBA
(alternative Interior angles)
angle BDC= 30° (Given)
Therefore, angle DBA = 30°
angle DBC = angle ADB
(alternative Interior angles)
angle DBC = 85°
Therefore, angle ADB = 85°
Now angle D = angle BDC + angle ADB
=>angle D = 30°+85°
Angle D = 115°
and In a Parallelogram, opposite angles are equal
=>angle D = angle B
Therefore angle B = 115°
and
Adjacent angles are supplementary in a Parallelogram
=>angle A + angle B = 180°
=>angle A + 115° = 180°
=>angle A = 180°-115°
=>angle A = 65°
In a Parallelogram, opposite angles are equal
=>angle A = angle C
=>angle C = 65°
Method-2:-
In the Parallelogram ABCD
angle BDC = 30° and angle DBC = 85°
We know that
The sum of all angles in a triangle is 180°
In ∆ BDC ,
angle BDC+angle DBC +angle DCB = 180°
=>30°+85°+angle DCB = 180°
=>115°+angle DCB = 180°
=>angle DCB = 180°-115°
=>angle DCB = 65°
and In a Parallelogram, opposite angles are equal
angle DCB =angle DAB = 65°
AB || CD and BD is a transversal then
angle BDC = angle DBA
(alternative Interior angles)
angle BDC= 30° (Given)
Therefore, angle DBA = 30°
angle DBC = angle ADB
(alternative Interior angles)
angle DBC = 85°
Therefore, angle ADB = 85°
angle angle BDC + angle ADB
=>angle D = 30°+85°
Angle D = 115°
and In a Parallelogram, opposite angles are equal
=>angle D = angle B
Therefore angle B = 115°
Answer:-
The all angles in the Parallelogram are
angle A = 65°
angle B = 115°
angle C = 65°
angle D = 115°
Used formulae:-
In a Parallelogram ,
- opposite angles are equal.
- Adjacent angles are supplementary
- If two Parallel lines are interested by a transversal then the pair of alternative interior angles are equal.