Question

one interior angle of a polygon is a right angle and each of the other interior angles is 126°. Calculate the number of sides of the polygon​

Answer 1

Answer:

Step-by-step explanation:

The total of angles and number of sides are related by the equation

t = 180(n - 2)

The total angles in this polygon t = 126n + 90

So:

180(n - 2) = 126n + 90

180n - 360 = 126n + 90

54n = 360 + 90 = 450

n = 8.333..

Looks like there's a mistake in the question as n should be a whole number.

Answer 2

Answer:

There are 7 sides.

Step-by-step explanation:

Let's Use the formula that states that the sum of the angles of an n-sided polygon is given by.

S=(n−2)180

Since we are given that the two angles are right, the angles and each of the remaining angles is 144.

And Therefore, the sum is:

S=90

(n−2)144

(n−2)180

=90

+90

+(n−2)144

⇒(n−2)180

−(n−2)144

=180

⇒(n−2)(180

−144

)=180

⇒(n−2)(36

=180

⇒n−2=

36

180

​⇒n−2=5

⇒n=5+2=7

Hence, the polygon has 7 sides.