5. The measures of two adjacent angles of a parallelogram are in the ratio 3:2. Find the measure of each
of the angles of the parallelogram.
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Answers
Given :-
Ratio of two adjacent angles of a parallelogram = 3 : 2
To Find :-
The measure of each of the angles of the parallelogram.
Analysis :-
Consider the common ratio as a variable.
Multiply the variable to the ratio.
Make an equation accordingly and get the value of the variable.
Substitute the value of the variable and substitute it in the two adjacent angles.
Since the opposite sides of a parallelogram are equal; the other two angles would also be the same.
Solution :-
Let the measures of two adjacent angles ∠A and ∠B be 3x and 2x respectively in parallelogram ABCD.
∠A + ∠B = 180°
Given that,
∠A = 3x
∠B = 2x
Substituting them,
3x + 2x = 180°
5x = 180°
Finding the value of x,
x = 180/5
x = 36°
Therefore, the value of x is 36°.
Opposite sides of a parallelogram are equal.
∠A = ∠C = 3x
= 3 × 36 = 108°
∠B = ∠D = 2x
2 × 36 = 72°
Therefore, the measure of each of the angles of the parallelogram are 108°, 72°, 108° and 72°.