Question

the angles of a quadrilateral are in A.P .find the measute of all angles .if the largest angle is 144

Answer 1

Hello!!! friend..

I will try to answer your question..

As we all know, A. P has a first term (a) and a common difference. ( d)
Let first term be a
second term = a+d
third term=a+2d
fourth term=a+3d
......and so on...

No. of angles is a quadrilateral =4
Up-to fourth term ,we have to find
first angle = a
second angle= a+d
third angle =a+2d
fourth angle=a+3d
So, largest angle is the fourth one
a+3d= 144
Total sum of all angles of a quadrilateral =360
Then a+a+d+a+2d+a+3d=360
a+a+d+a+2d+144=360
3a+3d=216
3(a+d)=216
a+d=72
a+3d-(a+d)=144-72
a-a+3d-d=72
2d=72
d=36

So, the difference between the angles is 36.
a+d=72
a=36
So, first angle is 36
second angle is 72
third angle is 108
and the fourth angle is 144

Here is your answer,...
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