Question

The angles of a Pentagon are in linear series with common difference 10°.work out the smallest angle of the pentagon.​

Answer 1

88°

Explanation:

the sum of the interior angles of a polygon is

sum = 180° (n - 2 ) ← n is the number of sides

here n = 5 ( sides of a pentagon ) , then

sum = 180° × 3 = 540°

----------------------------------------------------

the angles are in a linear series which means an arithmetic sequence

the sum to n terms of an arithmetic sequence is

`S_(n)` =
`(n)/(2)` [ 2a₁ + (n - 1)d ]

where a₁ is the first angle and d the common difference

here d = 10 and S₅ = 540 and a₁ has to be found

`(5)/(2)` [ 2a₁ + (n - 1)d ] = 540

`(5)/(2)` [ 2a₁ + (4 × 10) ] = 540 ( multiply both sides by 2 to clear the fraction )

5(2a₁ + 40) = 1080 ( divide both sides by 5 )

2a₁ + 40 = 216 ( subtract 40 from both sides )

2a₁ = 176 ( divide both sides by 2 )

a₁ = 88

The smallest angle of the pentagon is 88°