Polygon – Problems on Interior & Exterior angle of a polygon with solution
Interior & Exterior angle of a polygon
In this lesson we will learn the,
(1) Solutions of problems on interior and exterior angles of a polygon.
Example 1: Find the sum of all interior angles in a regular triangle (3-sided).
Solution:
Step 1: Write the formula
Sum of interior angles of a polygon = (n-2) x 180o
where n is number of sides.
In this problem number of sides in the given polygon is 3, so n = 3.
Step 2: Put the values in the formula
= (3 – 2) x 180
= 1 x 180
= 180o
Answer: The sum of the interior angles of a triangle is
Example 2: Find the sum of all interior angles in a regular pentagon (5-sided).
Solution:
Step 1: Write the formula
Sum of interior angles of a polygon = (n-2) x 180o
where n is number of sides.
In this problem number of sides in the given polygon is 5, so n = 5.
Step 2: Put the values in the formula
= (5 – 2) x 180
= 3 x 180
= 540o
Answer: The sum of the interior angles of a pentagon is 540º
Example 3: Find the sum of all interior angles in a regular octagon (8-sided).
Solution:
Step 1: Write the formula
Sum of interior angles of a polygon = (n-2) x 180o
where n is number of sides.
In this problem number of sides in the given polygon is 8, so n = 8.
Step 2: Put the values in the formula
= (8 – 2) x 180
= 6 x 180
= 1080o
Answer: The sum of the interior angles of a octagon is 1080º
Example 4: Find the sum of all interior angles in a 12 sided (regular polygon 12-sided).
Solution:
Step 1: Write the formula
Sum of interior angles of a polygon = (n-2) x 180o
where n is number of sides.
In this problem number of sides in the given polygon is 12, so n = 12.
Step 2: Put the values in the formula
= (12 – 2) x 180
= 10 x 180
= 1800o
Answer: The sum of the interior angles of a pentagon is 1080º
Example 5: Find the interior angle of a regular octagon (8-sided).
Solution:
Step 1: Write the formula
Sum of interior angles of a polygon = (n-2) x 180o
where n is number of sides.
In this problem number of sides in the given polygon is 8, so n = 8.
Step 2: Put the values in the formula
= (8 – 2) x 180
= 6 x 180
= 1080o
In a regular octagon, all interior angles are congruent, so all angles have same measure.
Therefore,
the interior angle of a regular octagon is = 1080/8 = 135o
interior angle of a regular octagon is = 135o.
Answer: The interior angle of a octagon is 135o.
Example 6: Find the fifth interior angle of a convex pentagon if it’s four interior angles are 35o, 85o, 135o and 115o.
Solution:
Step 1: Write the formula
Sum of interior angles of a polygon = (n-2) x 180o
where n is number of sides.
In this problem number of sides in the given polygon is 5, so n = 5.
Step 2: Put the values in the formula
= (5 – 2) x 180
= 3 x 180
= 540o
Therefore, subtract the sum of four angles in order to get to fifth angle.
The given four angles are 35o, 85o, 135o and 115o.
Thus the fifth angle is = 540 – (35 + 85 + 135 + 115)
The sum of given four angles = 35 + 85 + 135 + 115
The sum of given four angles = 370o
Thus the fifth angle is = 540 – (35 + 85 + 135 + 115)
Thus the fifth angle is = 540 – 370
the fifth angle is = 170o
Answer: The fifth angle of the pentagon is 170o
Example 7: Find the sum of all interior angles in a regular hexagon (6-sided).
Solution:
Step 1: Write the formula
Sum of interior angles of a polygon = (n-2) x 180o
where n is number of sides.
In this problem number of sides in the given polygon is 6, so n = 6.
Step 2: Put the values in the formula
= (6 – 2) x 180
= 4 x 180
= 720o
Answer: The sum of the interior angles of a hexagon is 720o.