Question

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

Options

• 176°

• 68°

•  112°

• 102°

Answer 1

Let the smallest angle of the parallelogram be x

Therefore, according to the given statement other angle becomes (2x - 24).

Also, the opposite angles of a parallelogram are equal.

Therefore, the four angles become x,(2x - 24) ,x and(2x - 24).

According to the angle sum property of a quadrilateral:

x +(2x  - 24) + x +(2X - 24) = 360°

                               6x - 48° = 360°

                              6x - 48° = 360° + 48°

                                      6x = 408°

`x = (408°)/6`

x = 68°

Thus, the other angle becomes

= [2(68) - 24]°

= 112°

Thus, the largest angle of the parallelogram are is 112°.

Hence the correct choice is (c).