Question

7. One angle of a quadrilateral is of 108° and the remaining three angles are equal. Find each of the three
equal angles
(NCERT Exemplar)
​

Answer 1

Given:-

• One angle of quadrilateral is 108°.
• Remaining angles are Equal.

To find:-

• Measure of remaining angles.

Solution:-

Let one of remaining angle be 'x'.

All three remaining angles will be x

[Beacuse it is given that remaining three angles are equal.]

We know that,

Sum of all angles of quadrilateral is 360°.

So,

➝ 108° + x + x + x = 360°

➝ 108° + 3x = 360°

➝ 3x = 360° - 108°

➝ 3x = 252°

➝ x = 252°/3

➝ x = 84°

Therefore,

Other three remaining angles will be of 84°.

Answer 2

Answer:

Let each of the three equal angles be x°.

Now, sum of angles of a quadrilateral = 360°

⇒ 108° + x° + x° + x° = 360° ⇒ 3x° = 360° – 108°

x° = 252°/3

⇒ x° = 84°

∴ x° = 84°

Hence, each of the three equal angles is 84°.