Question

07
Seccion B
The measures of two adjacent angles of a parallelogram-are in the ratio 3:2. Find the
measure of each of the angles of parallelogram.​

Answer 1

Answer:-

The angles are 108°, 72°, 108° And 72° Respectively.

Explanation:-

Given:-

• Ratio of two adjacent angles of a parallelogram = 3:2.

To Find:-

• Each angle of the parallelogram.

Concept Used:-

• In a parallelogram sum of adjacent angles is always equal to 180°.

• In a parallelogram opposite amgles are equal.

Now,

Since the ratio of adjacent angle is 3:2 so let the angles be 3x and 2x.

Also We know that sum of adjacent angles is equal to 180°.

↦ 2x + 3x = 180°.

↦ 5x = 180°.

↦ x = 180°/5.

↦ x = 36°.

Therefore the adjacent angles will be:-

• 3x = 3 × 36° = 108°.

• 2x = 2 × 36° = 72°.

Also,

Since the opposite angle sof the parallelogram are equal and hence all the angles of the parallelogram will be 3x, 2x, 3x and 2x which are 108°, 72°, 108° And 72° Respectively.

So each angles of the parallelogram are 108°, 72°, 108° And 72°.

Answer 2

Answer:

Let the measures of two adjacent angles, ∠A and ∠B, of parallelogram ABCD are in the ratio of 3:2.

Let ∠A = 3x and ∠B = 2x

We know that the sum of the measures of adjacent angles is 180º for a parallelogram.

∠A + ∠B = 180º

3x + 2x = 180º

5x = 180º

∠A = ∠C = 3x = 108º (Opposite angles)

∠B = ∠D = 2x = 72º (Opposite angles)

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