Question

One exterior angle formed on producing side of a parallelogram is 40 degrees.Find interior angles

Answer 1

Answer:40, 140 ,40 and 140 (all in degrees)

Step-by-step explanation:

Answer 2

The interior angles of ||gm are 40°,40°,140° ,and 140°.

Given:

• One exterior angle formed on the producing side of a parallelogram is 40°.

To find:

• Find interior angles

Solution:

Concept/Formula to be used:

• Find the interior angle against the given exterior angle.
• Apply properties of parallelogram to find other interior angles.

Step 1:

Find the interior angle $\angle D$.

*See the attachment.

Apply linear pair property;

$\angle EDA+\angle ADC=180^{\circ}$

$\angle ADC=180^{\circ}-40^{\circ}$

$\bf \angle ADC=\angle D=140^{\circ}$

Step 2:

Find other interior angles of parallelogram.

According to the property of the parallelogram,

The sum of adjacent angles of ||gm is 180°.

$\angle D+\angle C= 180^{\circ}$

$\angle C= 180^{\circ}-140^{\circ}$

$\bf \angle C= 40^{\circ}$

Opposite angles of ||gm are equal.

So,

$\bf \angle C=\angle A= 40^{\circ}$

$\bf \angle D=\angle B= 140^{\circ}$

Thus,

The interior angles of ||gm are 40°,40°,140° ,and 140°.

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