Question

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.

Answer 1

Measure of each angles

The parallelogram has four sides and three angles. The most important property of the parallelogram is that "The sum of two adjacent angles of the parallelogram is always equal to 180 degrees." The opposite angles or vertices of a parallelogram are congruent means equal.

We've been given that the measures of two adjacent angles of a parallelogram are 3:2. With this information we've been asked to find out the measure of each of the angles of the parallelogram.

Let's suppose that, the measure of two adjacent angles be $3x$ and $2x$ respectively.

After assuming we have two angles. So by using the angles sum property of adjacent angles of parallelogram we can easily get our measure of each angles of a parallelogram.

By using the angles sum property of adjacent angles of parallelogram and substituting all the available angles, we get:

$\implies 3x + 2x =180 \\ \\ \implies 5x =180 \\ \\\implies x = \cancel\dfrac{180}{5} \\ \\ \implies \boxed{x = 36^{\circ} }$

Now substituting the value of $x$ in both adjacent angles of parallelogram, we get:

• 3x = 3 * 36 = 108°
• 2x = 2 * 36 = 72°

We know that the opposite angles or vertices of a parallelogram are congruent. So our both angles of a parallelogram will be equal to opposite angles.

Therefore, the measure of each angles of the parallelogram is 108°, 72° 108° and 72°.

Answer 2

Given :-

The measures of two adjacent angles of a parallelogram are in the ratio of 3:2

To Find :-

The Measure of each of the angles of the parallelogram.

Solution :-

Let the angles be 3x and 2x

∠A + ∠B = 180°

3x + 2x = 180°

5x = 180°

x = 180/5

x = 36°

Now here,

∠A =  ∠C

∠A = 3x

= 3(36)

= 108°

∠A = ∠C = 108°

∠B = ∠D

∠B = 2x

∠B = 2(36)

∠B = 72°

∠B = ∠D = 72°

Hence

∠A = 108°

∠B = 72°

∠C = 108°

∠D = 72°