A regular polygon has an exterior angle of 4 degrees. what is the sum of its interior angles?
Answers
Answer:
Step-by-step explanation:
et x be the exterior angle of a regular polygon and y be the corresponding interior angle of a polygon.
Given that exterior angle is one fourth of its interior angle.
⇒x=
4
y
...(1)
Since x and y are exterior and corresponding interior angles, we have,
x+y=180
∘
⇒
4
y
+y=180
∘
⇒
4
5y
=180
∘
⇒y=
5
180
∘
×4
=144
∘
⇒x=180
∘
−y=180
∘
−144
∘
=36
∘
If each exterior angle of a regular polygon is A
∘
then the number of sides in the polygon=
A
360
∘
Since exterior angle is 36
∘
, the number of sides in the polygon=
36
∘
360
∘
=10
Answer:
Square = 90° × 4 = 360°
Step-by-step explanation:
Exterior angel = 180°- interior angel
180° - 150°
=30°
sum of angles =exterior angle ×n
30°×12
=360°