Question

if one angle of a parallelogram is 24 degrees less than twice the smallest angle then the largest angle of the parallelogram is

Answer 1

First of all as parallelogram is a quadrilateral with opposite sides parallel so we can say the opposite angles are also parallel that is a parallelogram consist of two pair with same angle.

Now let x be the smallest angle of the parallelogram, Also as explained above there must be another angle equal to x as it is a parallelogram.

we remaining with two angles.

Now also it is given that the other angle is 24° less than twice of the smallest.

So we get angle to be

2x-24°

And same as x there must be another angle equal to 2x-24°

And as sum of all the angles of quadrilateral is 360°.

So adding all and euating with 360°.

2x-24+2x-24+x+x=360

6x=360+48

6x=408

x=68°

So the largest angle from here can be deduced

2*68–24

Which comes to be 112°.

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Answer 2

Let the first angle be a

Second angle = 2a - 24

Now,

We know that,

Adjacent angles of paralellogram are suplementry

=> a + 2a - 24 = 180

=> 3a = 204

=> a = 68


Smaller angle = 68°

Larger angle = 112°