Question

Find the largest angle of a parallelogram, if one of its angles is 27° less than twice its smallest angle.

Answer 1

Given :
One angle is 27 less than twice the smallest angle

To find ,
The largest angle

Solution,
We know that ,
Sun of adjacent angles of a parallelogram is 180

Let the smallest angle be s

Then the other angle is 2s -27

We know,
s+ (2s-27)= 180
3s=180+27
3s=207
s=207/3
s=69

Therefore the other angle is
2(69)-27=111


Therefore the largest angle of the parallelogram is 111.

Answer 2

Correct answer:-

Let x

∘

be the smallest angle of the parallelogram.

According to the question, the largest angle is (2x

∘

−24

∘

).

It is known that the sum of the adjacent angles of the parallelogram is 180

∘

. Then,

x

∘

+2x

∘

−24

∘

=180

∘

3x

∘

=180

∘

+24

∘

3x

∘

=204

∘

x

∘

=68

∘

Therefore, the largest angle is (2(68

∘

)−24

∘

)=112

∘

.

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