Math, asked by hgsrky79551, 3 days ago

The measures of the exterior angles of a pentagon are x ° x°, 2 x ° 2x°, 4 x ° 4x°, 8 x ° 8x°, and 9 x ° 9x°. Find the measure of the largest exterior angle.

Answers

Answered by yashdhanik1122
0

Answer:

A ratio of 1:2:3:4:5 means that the measures of the angles can be expressed as 1x, 2x, 3x, 4x and 5x.

But this figure is a pentagon, meaning it is a polygon with 5 sides.

A 5 sided polygon can be chopped up into 3 triangles -- draw it! 3 triangles at 180 degrees each have a total of 540 degrees.

This means that x+2x+3x+4x+5x = 15x = 540 or x = 36.

So the angles are 36, 72, 108, 144, 180.

Since one of the five angles is 180, it means that this is not a pentagon. So the premise of the question is false.

But that was an illustration -- it's wrong!

The question asked about the exterior angles, not the interior angles. Those guys add up to 360 which mens we can apply our ratio to angle measure principle above but 15x = 360, not 540.

So x is 24 and the exterior angles are 24, 48, 72, 96, 120.

From the above you should be able to answer any question about any polygon's exterior or interior angles.

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