Question

the four angles of a quadrilateral are in arithmetic progression . whose common difference is 10degree find angles

Answer 1

1st angle = a
2nd angle = a+10
3rd angle = a+2*10 = a+20
4th angle = a+3*10 = a+30

All angls of quadrilateral sum to 360°
Now,
a+a+10+a+20+a+30 = 360
4a+60 = 360
4a = 300
a = 75

Angles are 75° , 85° , 95° , 105°

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Answer 2

See let the smallest angle of them be ‘x’
So, second angle = x + 10 ( since there is a difference of 10)
And third angle = x + 10 + 10 = x+20
And fourth = x + 20 + 10 = x +30
Now since it is a quadrilateral it has four angles and the sum of all of them must be 360
So, x + x+10 + x+20 + x+30 = 360
So, 4x + 60 = 360
So, 4x = 360 - 60
So, 4x = 300
So, x = 300/4
Therefore, x = 75
So first angle = x = 75
Second angle = x + 10 = 85
Third angle = x + 20 = 95
And, fourth angle = x + 30 = 105