Three of the exterior angles of an n-sided polygon are 50 degrees each, two of its interior angles are 127 degrees and 135 degrees, and the remaining interior angles are 173 degrees each. Find the value of n.

the exterior angles have to sum to 360, all the way around

with exterior of 50 we have exterior of 150 so far and 360 - 150 = 210 left for exterior angles
exterior with 127 interior = 53
exterior with 135 = 45
so
210 - 53 - 45 = 112 left for exteriors

exterior with 173 = 180-173=7
112/7 = 16
so i have
16
+1
+1
+3
= 21 interior angles = n

the sum of ext angle of a n sided polygon is 360

3(50)+(180_127)+(180-135)+(n_5)+180-173)
150+53+45+(n+5)(7)=360
248+7n-35=360
248-35+7n=360
213+7n=360
7n=360-213
7n=147
n=147/7
n=21 degree ans!!!!

The sum of ext. angle of a 'n' sided polygon is 360So, there are three exterior angles which are 50°. We have to find all the ext. angles first. So, find int. angle 127 ext. angle first, 180-127 = 53°.

Find int. angle 135 ext. angle aswell 180-135 = 45°.
There are 5 known ext. angles (three are 50°, one is 53°, and one is 45°) that is why we put n-5, because 5 angles have been given (we do not put 173 as we dont know how many 173° angles there are).
3(50)°+(180-127)°+(180-135)°+(n_5)×(180-173)°=360°
150°+53°+45°+(n+5)(7)°=360
248+n×7-5×7 =360°. (We have opened the brackets)
248°+7n-35°=360°
248°-35°+7n=360°
213°+7n=360°
7n=360°-213°
7n=147°
n=147÷7°
n=21

Hope this helps!

But Aysha I didn’t understand that where did (n_5) comes from

Good

Thank you!!!

Three of the exterior angles of an n sided polygon are 50 each, two of its interior angles are 127 and 135 and the remaining exterior angles are 173 each. What is the value of n?

Solution: The sum of the exterior angles of any polygon is always 360 deg.

Here, 3 exterior angles are 50 deg. each and so their sum = 150 deg. Two other exterior angles are 180–127 or 53º and 180–135 or 45º. Therefore the sum of the 5 exterior angles is 150+53+45 = 248º.

The sum of the remaining exterior angles = 360–248 or 112º. These are of the 112/(180–173) = 112/7 = 16 angles.

Hence n = 5+16 or 21. Answer.

OR
the exterior angles have to sum to 360, all the way around
with exterior of 50 we have exterior of 150 so far and 360 - 150 = 210 left for exterior angles
exterior with 127 interior = 53
exterior with 135 = 45
so
210 - 53 - 45 = 112 left for exteriors

exterior with 173 = 180-173=7
112/7 = 16
so i have
16
+1
+1
+3
= 21 interior angles = n
Hope this helped you!!!

I interpreted " two of its interior angles are 127 degrees and 135 degrees, and the remaining interior angles are 173 degrees each. " the wrong then.

so I should have had

130 + 130 + 130 + 127 + 135 + 173(n-5) = 180(n-2)
which gives
652 + 173n - 865 = 180n - 360

n = 21

sorry about the confusion
Damon is correct!

I didn't understand ayesha from where 35 came from .

this solution is correct