The sum of the angles marked by arrows is indeed equal to 360° as proved.
How to prove that the sum of the angles marked by arrows is 360°?
To prove that the sum of the angles marked by arrows is 360° we will follow the steps below;
let the interior angles = a, b and c
let the marked angles = x, y and z
The sum of the interior angles is calculated as;
a + b + c = 180
Since each interior angle is supplementary to each exterior angle we will have;
a = 180 - x (sum of angles on a straight line)
b = 180 - y (sum of angles on a straight line)
c = 180 - z (sum of angles on a straight line)
we will substitute the new values of a, b, and c into the original equation.
a + b + c = 180
(180 - x) + (180 - y) + (180 - z) = 180
540 - x - y - z = 180
- x - y - z = 180 - 540
- x - y - z = - 360
- (x + y + z) = - 360
divide through by (-1)
x + y + z = 360 (proved).