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

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Solution

Let the smallest angle of the parallelogram be

Therefore, according to the given statement other angle becomes .

Also, the opposite angles of a parallelogram are equal.

Therefore, the four angles become ,,and.

According to the angle sum property of a quadrilateral:

Thus, the other angle becomes

Hence, the four angles of the parallelogram are , , and .

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Similar questions

If one angle of a parallelogram is $24^{\circ}$ less than twice the smallest angle, then the measure of the largest angle of the parallelogram is

30^{\circ}

15^{\circ}

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