Question

The angles of a quadrilateral are in A. P. If the largest angle is 150,find other angles​

Answer 1

Answer:

Let angles be a,b,c,d

We know that,

$a + b + c + d = 360$

And angles are in A.P., then

$2b = a + c \\ 2c = b + d$

Given that largest angle is 150 then d will be largest angle

$a + b + c + d = 360 \\( a + c) + b + d = 360 \\ 2b + b + d = 360 \\ 3b + d = 360 \\3 b + 150 = 360 \\ 3b = 210 \\ b = 70$

$we \: know \: \\ 2c = b + d \\ 2c = 70 + 150 \\ 2c = 220 \\ c = 110$

$now \: \\ from \: \\ 2b = a + c \\ 2(70) = a + 110 \\ 140 = a + 110 \\ a= 140 - 110 \\ a = 30$

《The other angles are 30,70 and 110》