Question

a polygon has two interior angles of 120 degree each and the others are 150 degree each calculate the number of sides and the sum of interior angles in a polygon​

Answer 1

10 sides and

1440° total of interior angles.

Explanation:

The number of degrees in a polygon (sum of interior angles) is:

(n - 2)×180

This is the total. Here, n is the number of sides (same as the number of angles)

In your question, 2 of the angles are 120° and the remaining angles are 150°.

If n is ALL the angles, then (n-2) is all the 150° angles because the other 2 are 120°

So we can write an equation:

Our polygon:

120°+120°+(n-2)150°

=

(n-2)180°

Combine like terms:

240+(n-2)150=(n-2)180

Use Distributive property.

240+150n-300=180n-360

Again, combine like terms.

300 = 30n

Divide.

10 = n

n is the number of sides (and angles).

Check:

Ten-sided shape:

(10-2)180

= 1440°

Our shape:

120°+120°+ 8(150°)

= 240° + 1200°

= 1440° Check!

Answer 2

• 10 sides
• angles total 1440°

Explanation:

The formula for the total of interior angles can be used together with the given angle values to write an equation for the number of sides.

Setup

The total of interior angles of an n-sided polygon is 180°×(n -2). In the given n-sided polygon, two angles are 120° and (n -2) angles are 150°. The total of angles is the same either way it is computed:

2×120 +(n -2)150 = (n -2)180

Solution

Subtracting (n-2)150, we have ...

240 = 30(n -2)

8 = n -2 . . . . . . . . divide by 30

10 = n . . . . . . . . add 2

The polygon has 10 sides.

The total of interior angles is ...

angle sum = 180°×(10 -2) = 1440°

The sum of interior angles is 1440°.