Question

If the interior angles of five sided polygon are in ratio 1:2:3:4:5, then sum of measures of smallest and largest angles is?

Answer 1

Answer:

Step-by-step explanation:

on removal of ratio sign put x

then sum of all angles of polygon = 360

ie

1x+2x+3x+4x+5x = 360

15x = 360

x = 360/15

x = 24

sum of measures of smallest and largest angles = 1x + 5x = 6x 6*24 = 144 answer

Answer 2

Answer:

The measure of the smallest angle  = 36 and the measure of the largest angle = 180

Step-by-step explanation:

Given,

The interior angles of a five-sided polygon are in the ratio  1:2:3:4:5.

Required to find,

The measures of the smallest and the largest angle of the polygon.

Recall the formula,

Sum of Interior Angles of a polygon = (n-2) x 180°, where n is the number of sides of the polygon

Solution:

Given, The interior angles of a five-sided polygon are in the ratio  1:2:3:4:5.

Then the angles are x,2x,3x,4x,5x

The sum of the interior angles = x+2x+3x+4x+5x = 15x

We know,

Sum of Interior Angles of a polygon = (n-2) x 180°, where n is the number of sides of the polygon

Here, the polygon has five sides, we have n = 5

Sum of Interior Angles = (5-2) x 180° = 3 x 180° = 540°

∴ 15x = 540°

x = $\frac{540}{15}$ = 36

Hence the angles of the polygon are 36,2×36,3×36,4×36,5×36

That is 36,72,108,144,180

∴The measure of the smallest angle  = 36 and the measure of the largest angle = 180

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