Question

An angle of a quadrilateral is 72 degree .the other three angles are equal .find the measurement of each of the equal angles .

Answer 1

Answer :-

• The measure of the equal angles are 36°, 36° and 36°.

Step-by-step explanation

To Find :-

• The equal angles of quadrilateral.

★ Solution

Given,

The three angles of quadrilateral are equal.

One angle is 72°

Assumption

Let us assume the equal angles of quadrilateral as (x)°, (x)° and (x)°.

We know,

Sum of all interior angles of quadrilateral measures 360°

∴ x + x + x + 72 = 360

According the question,

⇒ x + x + x + 72 = 360

⇒ 3x + 72 = 360

⇒ 3x = 360 - 72

⇒ 3x = 108

⇒ x = 108/3

⇒ x = 36

We got, The value of x as 36.

Therefore,

The equal angles of quadrilateral are :-

⇒ x = 36°

⇒ x = 36°

⇒ x = 36°

The equal angles are 36°, 36 and 36°.

________________________________

VERIFICATION

• x + x + x + 72 = 360

By putting the value of x in L.H.S :-

⇒ x + x + x + 72

⇒ 36 + 36 + 36 + 72

⇒ 72 + 36 + 72

⇒ 108 + 72

⇒ 180 = L.H.S

Now, L.H.S = R.H.S = 180

Hence, Verified!

Answer 2

96° would be the measurement of each angle.

Step-by-step explanation:

Given that,

One angle of a quadrilateral = 72°

All other three angles are equal

To find,

The values of the other three angles = ?

Let each angle be x

As we know that the sum of four angles of a quadrilateral is 360°. So,

x + x + x + 72° = 360°

⇒ 3x = 360° - 72°

⇒ 3x = 288

∵ x = 96°

Thus, the value of each of the three angles is 96°.

Learn more: find the angle

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