Question

22. The angle measures of an octagon are in arithmetic sequence.
(a) What is the sum of its angles ?
(b) What is the sum of its smallest and largest angles ?
(c) If the difference between the smallest and largest angles is 70°, what is the measure
of smallest angle?​

Answer 1

Answer:1080°, 270°, 100° & 170°

Step-by-step explanation:

The sum of all angles in a polygon with n sides is given as (n-2)*180

For n= 8 in octagon as it has 8 sides.

Sum of angles hence will be 1080°.

For the angles given in arithmetic sequences the angles will be in ap. And here must be 8 terms in the ap as there are 8 angles. Hence the largest and smallest angle will be first and last term of the ap.

Hence difference between largest and smallest angle is

a+7d-a= 70

Hence d= 10

a + a+7d is sum of first and last term

Sum of all angles is the sum of all terms of ap which is

n/2(a+a+7d) = 1080

4(2a+70) =1080

2a=200

a=100

Hence the last angles or largest angle will be 170°

Smallest angle = 100°

Sum of smallest and largest angle 270°