Question

the angles ofa quadrilateral are in the arithmetic progression. the difference between the largest and the smallest angles is 60 degrees.what is the sum of the other two angles

Answer 1

Since angles are in AP,

So, all 4 respective angles will be

a, a+d, a+ 2d, a+ 3d

Here, d is common difference = 20° & the sum of all 4 angles = 360°

=> a + a+20 + a+ 40 + a + 60 = 360

=> 4a + 120 = 360

=> 4a = 240

=> a = 60

So angles are, 60° , 80° , 100° , 120° ……..ANS

Answer 2

● GIVEN THAT THE ANGLES OF QUADRILATERAL ARE IN AP. :-

» let's the angles of Quadrilateral are =

=> a, a+d, a+2d, a+3d

» and it's given that

=> (a+3d) - a = 60

=> 3d = 60

=> d = 60/3 = 20. ______[Eq(1)]
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» We know that :-

=> a + (a+d) + (a+2d) + (a+3d) = 360

=> 4a + 6d = 360

=> 4a + 6×20 = 360

=> 4a + 120 = 360

=> 4a = 360 - 120 = 240

=> a = 60

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» Hence the angle are :-

=> a = 60
=> a+d = 60 + 20 = 80
=> a+2d = 60+40 = 100
=> a+3d = 60+60 = 120
__________________[ANSWER]

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