One angle of a pentagon is $140^{o}$ . If the remaining angles are in the ratio $1 : 2 : 3 : 4$ . What is the size of the largest angle?

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Solution

Sum of interior angles of pentagon is 540

Given one angle 140 and other angles in ratio 1 : 2 : 3 ; 4

Let the other angles be x,2x,3x,4x

x + 2x + 3x + 4x + 140 = 540

10x = 540 - 140 = 400

x = 40

So largest interior angle is 4x = 4 * 40 = 160 degrees.

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One angle of a pentagon is 140o. If the remaining angles are in the ratio 1:2:3:4. What is the size of the largest angle?

Sum of interior angles of pentagon is 540 Given one angle 140 and other angles in ratio 1 : 2 : 3 ; 4Let the other angles be x,2x,3x,4x x + 2x + 3x + 4x + 140 = 540 10x = 540 - 140 = 400 x = 40 So largest interior angle is 4x = 4 * 40 = 160 degrees.

One angle of a pentagon is $140^{o}$ . If the remaining angles are in the ratio $1 : 2 : 3 : 4$ . What is the size of the largest angle?

Sum of interior angles of pentagon is 540

Given one angle 140 and other angles in ratio 1 : 2 : 3 ; 4

Let the other angles be x,2x,3x,4x

x + 2x + 3x + 4x + 140 = 540

10x = 540 - 140 = 400

x = 40

So largest interior angle is 4x = 4 * 40 = 160 degrees.