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.

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 pentagon with 5 sides: n = 5 The sum of its interior angles is: (2 x 5 \- 4) x 90° = (10 \- 4) x 90° = 6 x 90° = 540° It is given that in a pentagon, two angles are 40° and 60°, and the remaining three angles are in the ratio 1 : 3 : 7. Let the pentagon be ABCDE, such that ∠A = 40° and ∠B = 60° Let the common factor of the remaining angles be a. Thus, the remaining angles are: ∠C = a, ∠D = 3a and ∠E = 7a. Therefore, ⇒ ∠A \+ ∠B \+ ∠C \+ ∠D \+ ∠E = 540° ⇒ 40° \+ 60° \+ a \+ 3a \+ 7a = 540° ⇒ 100° \+ 11a = 540° ⇒ 11a = 540° \- 100° ⇒ 11a = 440° ⇒ a = ⇒ a = 40° Thus: ∠C = a = 40° ∠D = 3a = 3 x 40° = 120° ∠D = 7a = 7 x 40° = 280° Hence, the largest angle is 280°.

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Mathematics

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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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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