A heptagon has four angles each of 132° and remaining three angles are equal. Find the size of each of the three angles.

It is given that a heptagon has four angles each of 132° and the remaining three angles are equal. According to the properties of a polygon, if a polygon has n sides, then each of its interior angles is (2n \- 4) x 90°. Heptagon has 7 sides, so n = 7, = (2 x 7 \- 4) x 90° = (14 \- 4) x 90° = 10 x 90° = 900° The sum of interior angles of the heptagon is 900°. Let each of the three equal angles be x°. So, ⇒ 132° \+ 132° \+ 132° \+ 132° \+ x° \+ x° \+ x° = 900° ⇒ 528° \+ 3x° = 900° ⇒ 3x° = 900° \- 528° ⇒ 3x° = 372° ⇒ x° = ⇒ x° = 124° Hence, each of the three equal angles is 124°.

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Mathematics

A heptagon has four angles each of 132° and remaining three angles are equal. Find the size of each of the three angles.

Geometrical Shapes

Related Questions

Three angles of a quadrilateral are in the ratio 4 : 5 : 6. The sum of the least and the greatest of these angles is 160°. Find all the angles of the quadrilateral.

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