Question

The measures of two adjacent angles of parallelogram are in the ratio
3:2. Find the measures of each angle.​

Answer 1

Answer:

one of the angle is 54° and another angle is 36°.

Step-by-step explanation:

let the angles ratio= x

thus one angle=3x

another angle=2x

we know that sum of adjacent angle=90

=>3x+2x=90

=>5x=90

=>x=90/5=18

one angle=3x=3×18=54°

another angle=2x=2×18=36°

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Answer 2

Answer:

Let the measures of two adjacents angles, <A and <B, of parallelogram ABCD are in ratio of 3:2

Let <A = 3x and <B = 2x

We know that the sum of adjacents angles is 180° for a parallelogram.

<A + <B = 180°

3x + 2x = 180°

5x = 180°

x = 180° / 5 = 36°

<A = <C = 3x = 180° ( Opposite angles )

<B = <D = 2x = 72° ( Opposite angles )

Thus, the measures of the angles of the parallelogram are 108°, 72°, 108° and 72°.