Polygon Angle Calculation
For any polygon, the internal angle and its corresponding external angle at a vertex add up to $180^\circ$. This is because they form a linear pair.
External Angle Property
The relationship is:
Internal Angle + External Angle = $180^\circ$
The question states that the external angle of the regular polygon is $72^\circ$.
Calculate Internal Angle
Using the property above, we can find the internal angle:
Internal Angle = $180^\circ$ - External Angle
Substitute the given value:
Internal Angle = $180^\circ - 72^\circ$
Internal Angle = $108^\circ$
Therefore, the internal angle of the regular polygon is $108^\circ$.
Similar Questions
- If the sum of the interior angles of a regular polygon is equal to four times the sum of its exterior angles, then what is the number of diagonals in the polygon?
- Find the ratio of the measure of an angle of a regular pentagon to that of a regular octagon.
- The area of an isosceles right angle triangle is $81 \text{ cm}^2$ . Find the length of its hypotenuse.
- In a polygon, the sum of the interior angles is triple the sum of the exterior angles. The number of sides is:
- What is the measure of each exterior angle of a regular octagon?
- The difference between the interior and exterior angles at a vertex of a regular polygon is $140^\circ$. The number of sides of the polygon is:
- The ratio of an interior angle to the exterior angle of a regular polygon is $4:1$. The number of sides of the polygon is:
- If the interior angles of a pentagon are in the ratio 1 : 3 : 5 : 7 : 11, then the measure of the smallest interior angle is:
- If the side of an equilateral triangle is 2 cm, then find the area and the altitude of the triangle.
- Two sides of a triangle are of lengths 4 cm and 10 cm. If the length of the third side is $a$ cm, then:
Important Questions from Geometry
If the angles of a triangle are in the ratio of 2:3:4, then the difference of the measure of greatest angle and smallest angle is
In ΔABC, ∠A = 90°, AD ┴ BC and AD = BD = 2 cm. The length of CD is
How many lines of symmetry does a rectangle have?
The number of diagonals in each face a cube is
Which of the following is/are the geometric figures with the line of symmetry?
I. Rectangle
II. Isosceles triangle
