Question

An anglr of a quadrilateral is 120 degree the other three angles are equal find the measure of each of the equal angles

Answer 1

Answer:-

Given:

Measure of one angle of a Quadrilateral = 120°.

And, the measures of other three angles are equal.

Let the measures of three angles be x.

We know that,

Sum of four angles of a Quadrilateral = 360°

⟹ 120° + x + x + x = 360°

⟹ 3x = 360° - 120°

⟹ 3x = 240°

⟹ x = 240/3

⟹ x = 80°

∴ The measure of other three angles is equal to 80°.

Additional Information:-

• A closed figure bounded by four line segments is called a Quadrilateral.

• Sum of four angles of a Quadrilateral = 360°.

• There are different types of quadrilaterals based on sides and angles.

• The line segments joining the opposite vertices of a Quadrilateral are called Diagonals.

Answer 2

Given:

• An angle = 120°
• Other three angles are equal

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Need to find:

• The angles =?

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Solution:

Let the equal angles measure = x

We know,

Sum of all the angles in a quadrilateral = 360°

⟹ 120° + x+ x+ x = 360°

⟹ 120° +3x = 360°

⟹ 3x = 360° -120°

⟹ 3x = 240°

⟹ $\red{\bold{\large{\boxed{x=80 \degree}}}}$

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Knowledge cell:

• If all the sides of a quadrilateral are equal then it's either a rohmbus or a square

• If all the angles of a quadrilateral are 90° then it's either a square or a rectangle

• If any two opposite sides of a quadrilateral are equal and parallel to each other then the quadrilateral is called a parallelogram

• Square, rohmbus, rectangle are special types of parallelogram