Name: Understanding Vertically Opposite Angles
Uploaded: 2019-07-19
Duration: 6 min 7 s
Description: Did you know that many examples of vertically opposite angles can be seen in our daily lives? A railroad crossing sign for example. So how do we define this...

Question

Two unequal angles of a parallelogram are in the ratio

2 : 3

Find all its angles in degrees.

Accepted Answer

The parallelogram can be drawn as follows:

It is given that,

$∠ A : ∠ C = 2 : 3$ .

Therefore, let:

$∠ A = 2 x$ and $∠ C = 3 x$ .

We know that opposite angles of a parallelogram are equal.

Therefore,

$∠ A = ∠ D$ . So, $∠ D = 2 x$ .

Similarly, $∠ B = 3 x$ .

Also, if $A B ∥ C D$ , then sum of consecutive interior angles is equal to $180 °$ .

Therefore,

$∠ A + ∠ C = 180 °$

$\Rightarrow 2 x + 3 x = 180 °$

$\Rightarrow 5 x = 180 °$

$\Rightarrow x = \frac{180 °}{5}$

$\Rightarrow x = 36 ° .$ .

We have,

$∠ A = 2 x$

$\Rightarrow ∠ A = 2 (36 °)$

$\Rightarrow ∠ A = 72 ° .$

Also,

$∠ C = 3 x$

$\Rightarrow ∠ C = 3 (36 °)$

$\Rightarrow ∠ C = 108 °$ .

Similarly, $∠ D = 72 °$ and $∠ B = 108 °$ .

Hence, the four angles of the parallelogram are as follows:

$∠ A = 72 °, ∠ B = 108 °, ∠ C = 72 °$ and $∠ D = 108 °$ .

Two unequal angles of a parallelogram are in the ratio $2 : 3$ Find all its angles in degrees.

Important Questions on Lines and Angles

Learn and Prepare for any exam you want !

Two unequal angles of a parallelogram are in the ratio 2:3 Find all its angles in degrees.

Important Questions on Lines and Angles

Learn and Prepare for any exam you want !

Two unequal angles of a parallelogram are in the ratio $2 : 3$ Find all its angles in degrees.