Question

The sum of the measures of seven angles of an octagon is 1000 degrees fine the measure of the eighth angle

Answer 1

Answer: 80°

Step-by-step explanation:

We know that the sum of all angles in a polygon having n sides is given by :

$(n-2)\times 180^{\circ}$

For octagon , n= 8

Then, the sum of all angle sin octagon = $(8-2)\times 180^{\circ}$

$=6\times 180^{\circ}$

$=1080^{\circ}$

It is given that , The sum of the measures of seven angles of an octagon is 1000 degrees.

Then, the measure of the eighth angle = Sum of all angles - 1000°  

= 1080° -  1000°  =80°

Hence, the measure of the eighth angle is 80° .

Answer 2

Now, we're assuming this is for interior angles.

the sum of all the interior angles in a polygon is

180(n - 2)   n = number of sides in a polygon.

now, this is an OCTAgon, it has OCTA=8 sides, so it has a sum of its interior angles at 180( 8 - 2) --> 180(6) ---> 1080°.

now, we already know seven of those eight angles add up to 1000, so... surely you'd know what the last one is.