Hey, I came across a different approach to solve the below mentioned question.
I was not quite satisfied with assuming the internal angles of the pentagon to be 108 without any additional information. I just plotted a random start shape and estimated the angles and the angles differed.
Consider the internal angles, which would defintely not be 108.
I came up with a different way to solve it using what Greg taught us about - the sum of internal angles of polygon. (n-2) * 180
The formula is applicable if it is a regular polygon, but we do not have enough information provided in the question which says it a regular one nor we can derive to a conclusion that it is an regular one.
I have attached the second screenshot to show that the polygon is not regular as angles are skewed.
I agree there is no reason to consider these to be regular polygons. Here is how I would approach it:
The sum of all external angle = 360 for all polygons
In the five triangles we have v,w,x,y,z plus 2 sets of external angles
v+w+x+y+z + 360 + 360 = 180 * 5
v+w+x+y+z = 180
But if you are conceptually strong, you would know that the answer would not change whether the polygons are regular or not, and in that case you will be easily able to apply Greg’s method
