The measure of two adjacent angle of parallelogram are in the ratio 3:2 . find the measure of each of the angle of parallelogram.
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Answers
Given:
The measure of two adjacent angles of a parallelogram is in ratio 3:2
To be found:
The measure of all angles of the parallelogram.
Here are some properties of a parallelogram-
- The sum of two adjacent angles of a parallelogram is 180°.
- The opposite sides of the parallelogram are equal and parallel.
- The opposite angles of the parallelogram are equal.
So,
Let one angle be 3x and other 2x
As
- The opposite angles of the parallelogram are equal
Then we have 2 angles as '3x' degree and 2 angles as '2x' degree. [There are four interior angles in a parallelogram]
Now,
As they are adjacent so,
⇒ 3x + 2x = 180
⇒ 5x = 180
⇒ x = 180 ÷ 5
⇒ x = 36
So,
The angles are
3x = 3 × 36 = 108°
And
2x = 2 × 36 = 72°
Now,
We have two same angles as 108° and two same angles as 72°
Hence
The angles of the parallelogram are 108°, 108°, 72°, and 72°
SOLUTION:-
Given
• Two adjacent angle of llgm are in ⠀⠀ratio 3:2
To find
• All angles of llgm
Explanation
Let Two adjacent angles A or B of llgm ABCD be 3x and 2x respectively.
Since
The adjacent angles of a llgm are Supplementary.
∠A+∠B= 180°
➡️ 3x+2x =180°
➡️ 5x=180°
➡️ x=180°/5
➡️ x= 36°
Angles are ⤵️
3x = 3×36° = 108°
2x = 2×36° = 72°
Since
Opposite Angles are equal in llgm
Therefore
∠C= ∠A= 108°
And
∠D= ∠B= 72°
Hence,
•∠A=108°
•∠B=72°
•∠C= 108°
•∠D= 72°
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