Question

An exterior angle and the interior angle of a regular polygon are in the ratio 2:7. Find the measures of interior and exterior angles.

Answer 1

Answer:

7+2 = 9. 180/9 = 20. Hence exterior angle is 20*2 = 40 degrees and the interior angle 20*7 = 140.

Step-by-step explanation:

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Answer 2

$\huge\mathcal\color{teal} Answer :-$

Let $7a =$ interior angle

 

$2a =$exterior angle

$7a + 2a = 180$

$=> 9a = 180$

$a = 20$

For a regular polygon of n sides , each exterior angle has a measure of $\frac{360}{n}$

Since the exterior angle of each angle has $a$ measure of $40°$, then the number of sides $n$

$n$ = $\frac{360}{n}$ = $9 sides$

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