Home
/
Math
/
1. The exterior angle of a regular polygon is 36^circ (a) How many sides does the have? (b)Calculate the sum of all the interior angles of this regular polygon.

Question

1. The exterior angle of a regular polygon is 36^circ 
(a) How many sides does the have?
(b)Calculate the sum of all the interior angles of this regular polygon.

1. The exterior angle of a regular polygon is 36^circ (a) How many sides does the have? (b)Calculate the sum of all the interior angles of this regular polygon.

expert verifiedVerification of experts

Answer

4.2189 Voting
avatar
GlennaProfessional · Tutor for 6 years

Answer

(a) The number of sides of the polygon is \( n = \frac{360}{36} = 10 \) sides.<br /><br />(b) The sum of all the interior angles of this regular polygon is \( (n-2) \times 180 = (10-2) \times 180 = 1440^{\circ} \).

Explain

## Step1:<br />The number of sides of a regular polygon can be found by dividing 360 degrees by the measure of each exterior angle. <br /><br />### \(n = \frac{360}{36} \)<br /><br />## Step2:<br />The sum of all the interior angles of a regular polygon can be calculated using the formula \((n-2) \times 180\), where \( n \) is the number of sides.<br /><br />### \( \text{Sum of interior angles} = (n-2) \times 180 \)
Click to rate: