Question

two adjacent angles of a parallelogram ABCD are in the ratio 2:3 . Find all the angles of the parallelogram .

question from understanding quadrilateral ​

Answer 1

In a parallelogram ABCD, two adjacent angles has been given, i.e., $2:3$. With this information, we have been asked to find out all the angles of the parallelogram.

Let us assume that, the two adjacent angles be $2x$ and $3x$ respectively.

We know that, the sum of the adjacent angles of a parallelogram is equal to ${180}^{\circ}$. Therefore,

$\implies 2x + 3x = 180 \\ \\ \implies 5x = 180 \\ \\ \implies x = \dfrac{180}{5} \\ \\ \implies x = 36$

So, the two adjacent angles will be:

$\implies \begin{cases} & 2x = 2 \times 36 = 72 \\ \\ & 3x = 3 \times 36 = 108 \end{cases}$

We know that, the opposite angles of a parallelogram are equal. Now, the angles of a parallelogram will be ${72}^{\circ}$, ${108}^{\circ}$, ${72}^{\circ}$ and ${108}^{\circ}$.

Hence, all the angles of a parallelogram is 72°, 108°, 72° and 108°.

Answer 2

Given :-

Two adjacent angles of a parallelogram ABCD are in the ratio 2:3

To Find :-

All angles

Solution :-

Let us assume that the adjacent angles of parallelogram are 2x and 3x

We know that

Sum of adjacent angles are 180°

⇒ 2x + 3x = 180

⇒ 5x = 180

⇒ x = 180/5

⇒ x = 36°

Angles of parallelogram are :-

2x = 2(36) = 72°

3x = 3(36) = 108°

2x = 2(36) = 72°

3x = 3(36) = 108°