The interior angles of a pentagon are in the ratio 4 : 5 : 6 : 7 : 5. Find each angle of the pentagon.

According to the properties of polygons, if a polygon has n sides, then the sum of its interior angles is (2n \- 4) x 90°. A pentagon have 5 sides. So, sum of its interior angles is: (2 x 5 \- 4) x 90° = (10 \- 4) x 90° = 6 x 90° = 540° It is given that the interior angles of the pentagon are in the ratio 4 : 5 : 6 : 7 : 5. Let each angle be a. So, 4a \+ 5a \+ 6a \+ 7a \+ 5a = 540° ⇒ 27a = 540° ⇒ a = ⇒ a = 20° The angles are: 4a = 4 x 20° = 80° 5a = 5 x 20° = 100° 6a = 6 x 20° = 120° 7a = 7 x 20° = 140° 5a = 5 x 20° = 100° Hence, the measures of the angles are 80°, 100°, 120°, 140° and 100°.

Find the sum of exterior angles obtained on producing the sides of a polygon, in order, with 7 sides.

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The sides of a hexagon are produced in order. If the measures of exterior angles so obtained are (6x - 1)°, (10x + 2)°, (8x+ 2)°, (9x - 3)°, (5x + 4)° and (12x + 6)°, find each exterior angle.

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Two angles of a hexagon are 120° and 160°. If the remaining four angles are equal, find each equal angle.

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The figure given below shows a pentagon ABCDE with sides AB and ED parallel to each other, and ∠B : ∠C : ∠D = 5 : 6 : 7.
(i) Using formula, find the sum of interior angles of the pentagon.
(ii) Write the value of ∠A + ∠E.
(iii) Find angles B, C and D.

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Mathematics

The interior angles of a pentagon are in the ratio 4 : 5 : 6 : 7 : 5. Find each angle of the pentagon.

Geometrical Shapes

Related Questions

Find the sum of exterior angles obtained on producing the sides of a polygon, in order, with 7 sides.

The sides of a hexagon are produced in order. If the measures of exterior angles so obtained are (6x - 1)°, (10x + 2)°, (8x+ 2)°, (9x - 3)°, (5x + 4)° and (12x + 6)°, find each exterior angle.

Two angles of a hexagon are 120° and 160°. If the remaining four angles are equal, find each equal angle.

The figure given below shows a pentagon ABCDE with sides AB and ED parallel to each other, and ∠B : ∠C : ∠D = 5 : 6 : 7.
(i) Using formula, find the sum of interior angles of the pentagon.
(ii) Write the value of ∠A + ∠E.
(iii) Find angles B, C and D.

Mathematics

The interior angles of a pentagon are in the ratio 4 : 5 : 6 : 7 : 5. Find each angle of the pentagon.

Geometrical Shapes

Related Questions

Find the sum of exterior angles obtained on producing the sides of a polygon, in order, with 7 sides.

The sides of a hexagon are produced in order. If the measures of exterior angles so obtained are (6x - 1)°, (10x + 2)°, (8x+ 2)°, (9x - 3)°, (5x + 4)° and (12x + 6)°, find each exterior angle.

Two angles of a hexagon are 120° and 160°. If the remaining four angles are equal, find each equal angle.

The figure given below shows a pentagon ABCDE with sides AB and ED parallel to each other, and ∠B : ∠C : ∠D = 5 : 6 : 7.(i) Using formula, find the sum of interior angles of the pentagon.(ii) Write the value of ∠A + ∠E.(iii) Find angles B, C and D.

The figure given below shows a pentagon ABCDE with sides AB and ED parallel to each other, and ∠B : ∠C : ∠D = 5 : 6 : 7.
(i) Using formula, find the sum of interior angles of the pentagon.
(ii) Write the value of ∠A + ∠E.
(iii) Find angles B, C and D.