Question

if one angle of a paralleogram is 24°less than twice the smallest angle,then the measure of the largest angle of the parallelogram is...

Answer 1

The question is absurd. There are only 2 angles in a parallelogram. So one can be larger and the other smaller. ‘Largest’ and ‘smallest’ are used when there are at least 3 values to be examined.

However, ignoring the grammatical mistake in the question, here is the solution.

There are two angles x and y.

x+y = 180 … (1)

y = 2x-24 … (2)

From (1), y = 180 -x. Put that value of y in (2) to get

180 - x = 2x - 24, or

3x = 180 + 24 = 204, or

x = 204/3 = 68 degrees.

The larger angle, y = 112 degrees.

Answer 2

Let the measure of the smallest angle = x.

Then the measure of the largest angle will be 24 less than twice the smallest angle.

(2x - 24).

We know that Adjacent angles of a parallelogram = 180.

x + (2x - 24) = 180

x + 2x - 24 = 180

3x - 24 = 180

3x = 24 + 180

3x = 204

x = 204/3

x = 68.

Therefore the largest angle = 2x - 24

                                               = 2*68 - 24)

                                               = 136 - 24

                                               = 112.


Therefore the measure of the largest angle of the parallelogram = 112 degrees.


Hope this helps!