Question

Find the sizes of the angles of a parallelogram if one angle is 20 less than twice the smallest angle​

Answer 1

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

∘

.

Step-by-step explanation:

thx ...

Answer 2

Let one angle be x

•°• other angle will 2x-20

As the theorem states,

"Opposite angles of parallelogram are equal."

and

"Sum of angles of parallelogram is 360°."

Sum of angles = 360°

$(x) + (x)+ (2x - 20) + (2x - 20) = 360$

$2x + 4x - 40 = 360 \\ 6x = 320 \\ x = \frac{320}{6} \\ x = 53.3$

other angle will be = 2x-20

=2(53.3)-20

=86.6°

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