The angles of a hexagon are x + 10°, 2x + 20°, 2x - 20°, 3x - 50°, x + 40° and x + 20°. Find x.

According to the properties of a polygon, if a polygon has n sides, then the sum of its interior angles is (2n \- 4) x 90°. For a hexagon with 6 sides, n = 6. The sum of its interior angles is: (2 x 6 \- 4) x 90° = (12 \- 4) x 90° = 8 x 90° = 720° It is given that the angles of the hexagon are x + 10°, 2x + 20°, 2x - 20°, 3x - 50°, x + 40° and x + 20°. ⇒ ∠A \+ ∠B \+ ∠C \+ ∠D \+ ∠E \+ ∠F = 720° ⇒ (x \+ 10°) \+ (2x \+ 20°) \+ (2x \- 20°) \+ (3x \- 50°) \+ (x \+ 40°) \+ (x \+ 20°) = 720° ⇒ x \+ 10° \+ 2x \+ 20° \+ 2x \- 20° \+ 3x \- 50° \+ x \+ 40° \+ x \+ 20° = 720° ⇒ 10x \+ 20° = 720° ⇒ 10x = 720° \- 20° ⇒ 10x = 700° ⇒ x = ⇒ x = 70° Hence, the value of x is 70°.

Two angles of a polygon are right angles and the remaining are 120° each. Find the number of sides in it.

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In a hexagon ABCDEF, side AB is parallel to side FE and ∠B : ∠C : ∠D : ∠E = 6 : 4 : 2 : 3. Find ∠B and ∠D.

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In a pentagon, two angles are 40° and 60° and the rest are in the ratio 1 : 3 : 7. Find the biggest angle of the pentagon.

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Each interior angle of a regular polygon is double of its exterior angle, the number of sides in the polygon is.
3
4
6
8

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Mathematics

The angles of a hexagon are x + 10°, 2x + 20°, 2x - 20°, 3x - 50°, x + 40° and x + 20°. Find x.

Geometrical Shapes

Related Questions

Two angles of a polygon are right angles and the remaining are 120° each. Find the number of sides in it.

In a hexagon ABCDEF, side AB is parallel to side FE and ∠B : ∠C : ∠D : ∠E = 6 : 4 : 2 : 3. Find ∠B and ∠D.

In a pentagon, two angles are 40° and 60° and the rest are in the ratio 1 : 3 : 7. Find the biggest angle of the pentagon.

Each interior angle of a regular polygon is double of its exterior angle, the number of sides in the polygon is.
3
4
6
8

Mathematics

The angles of a hexagon are x + 10°, 2x + 20°, 2x - 20°, 3x - 50°, x + 40° and x + 20°. Find x.

Geometrical Shapes

Related Questions

Two angles of a polygon are right angles and the remaining are 120° each. Find the number of sides in it.

In a hexagon ABCDEF, side AB is parallel to side FE and ∠B : ∠C : ∠D : ∠E = 6 : 4 : 2 : 3. Find ∠B and ∠D.

In a pentagon, two angles are 40° and 60° and the rest are in the ratio 1 : 3 : 7. Find the biggest angle of the pentagon.

Each interior angle of a regular polygon is double of its exterior angle, the number of sides in the polygon is.3468

Each interior angle of a regular polygon is double of its exterior angle, the number of sides in the polygon is.
3
4
6
8