Three exterior angles of a pentagon measures 60,80and 90.Find the measure of other two exterior angle, assuming them equally Thanks!

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Mathematics Thu Nguyệt 3 years 2021-07-31T14:41:10+00:00 2021-07-31T14:41:10+00:00 1 Answers 176 views 0

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bonexptip · Answer 1 · 2021-07-31T14:43:06+00:00

bonexptip

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2021-07-31T14:43:06+00:00 July 31, 2021 at 2:43 pm

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Given:

The three exterior angles of a pentagon measures 60,80 and 90.

To find:

The measure of other two exterior angle, assuming them equally.

Solution:

Let x be the measure of two other exterior angles of the pentagon.

We know that the sum of all exterior angles of a pentagon is 360 degrees.

$60^\circ+80^\circ+90^\circ+x+x=360^\circ$

$230^\circ+2x=360^\circ$

$2x=360^\circ-230^\circ$

$2x=130^\circ$

Divide both sides by 2.

$\dfrac{2x}{2}=\dfrac{130^\circ}{2}$

$x=65^\circ$

Therefore, the measures of both exterior angles are 65 degrees.