Answer : The sum of the measure of the interior angle of a dodecagon is, 1800°
Step-by-step explanation :
As we know that a circle makes a complete angle of 360° at the center.
As the dodecagon is a plane figure that has 12 sides.
When the lines join from center to edges of the figure then 12 triangles will be formed.
So, each angle at the center of dodecagon = [tex]\frac{360^o}{12}=30^o[/tex]
The triangles formed in the figure will be an isosceles triangle that has two equal sides and their corresponding angles are also equal.
Now we have to take a triangle to calculate the interior angle of dodecagon.
As we know that the sum of interior angles of a triangle is equal to 180°.
So,
∠A + ∠B + ∠O = 180°
As, ∠A = ∠B and ∠O = 30°
2∠A + ∠O = 180°
2∠A + 30° = 180°
2∠A = 150°
∠A = 75°
Each of the interior angle of dodecagon = 2 × ∠A
Each of the interior angle of dodecagon = 2 × 75°
Each of the interior angle of dodecagon = 150°
The sum of the measure of all interior angle of a dodecagon = 12 × 150° = 1800°
Hence, the sum of the measure of the interior angle of a dodecagon is, 1800°
