Question

Find the measure of all the angles of a parallelogram, if one angle is 24° less than the twice
of 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

∘