If the ratio of angles in the pentagon are in the ratio 1- 2- k - 3- k - k -1- k -3 k -1- Then the measure of the smallest angle of the pentagon will be -A- Proportional to 1 - k 2B- Proportional to kC- Proportional to k 2D- Proportional to 1 - kE- Independent of k

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If the ratio ...

Question

If the ratio of angles in the pentagon are in the ratio 1 : 2--k : 3--k : k+ 1 : k + 3 (k<1). Then the measure of the smallest angle of the pentagon will be -

Proportional to k

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Proportional to k²

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Proportional to 1/k

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Independent of k

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Proportional to 1/k²

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Solution

The correct option is D
Independent of k

Sum of angles of a pentagon = 540 $^{0}$ Let the measure of the smallest angle be `x' x + (2-k)x + (3-k)x + (k+1)x +(k+3)x = 540 $^{0}$ x = 54 $^{0}$ $∴$ The smallest angle is independent of k.

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If the ratio of angles in the pentagon are in the ratio 1 : 2--k : 3--k : k+ 1 : k + 3 (k<1). Then the measure of the smallest angle of the pentagon will be -

The correct option is D Independent of k Sum of angles of a pentagon = 5400 Let the measure of the smallest angle be `x' x + (2-k)x + (3-k)x + (k+1)x +(k+3)x = 5400 x = 540 ∴The smallest angle is independent of k.

The correct option is D
Independent of k

Sum of angles of a pentagon = 540 $^{0}$ Let the measure of the smallest angle be `x' x + (2-k)x + (3-k)x + (k+1)x +(k+3)x = 540 $^{0}$ x = 54 $^{0}$ $∴$ The smallest angle is independent of k.