Question

A quadilateral ABCD has all its angles of the same measure. What is the measure of each angles​

Answer 1

Answer :

›»› The measure of each angles is 90°.

Given :

• A quadilateral ABCD has all its angles of the same measure.

To Find :

• The measure of each angles.

Solution :

Here in this question we have to find the measure of each angles. So, we need to consider the measure of each angles as a variable, then we will find the measure of each angles on the basis of conditions given above.

Let,

The measure of each angles be "x"

As we know that

Sum of all the angles of a quadilateral is 360°

→ x + x + x + x = 360

→ 2x + x + x = 360

→ 3x + x = 360

→ 4x = 360

→ x = 360/4

→ x = 90

║Hence, the measure of each angles is 90°.║

Verification :

Sum of all angles is 360°

→ 90 + 90 + 90 + 90 = 360

→ 180 + 90 + 90 = 360

→ 270 + 90 = 360

→ 360 = 360

Here, LHS = RHS

Hence Verified !

Answer 2

Answer :-

• Measure of each of the angles is 90°.

Given :-

• A quadilateral ABCD has all its angles of the same measure.

To Find :-

• Measure of each angles.

Solution :-

Here all angles are equal

So consider all angles as x

As we know that

Sum of all angles of a quadrilateral is 360°

According to question :-

⇒ x + x + x + x = 360

⇒ 2x + x + x = 360

⇒ 3x + x = 360

⇒ 4x = 360

⇒ x = 360/4

⇒ x = 90°

Hence, measure of each of the angles is 90°.