The diagonal of the parallelogram makes angles of 28∘ and 68∘ with its sides. Find the smaller angle
| April 4, 2021 | education
The diagonal of the parallelogram makes angles of 28∘ and 68∘ with its sides. Find the smaller angle of the parallelogram.
By the condition of the problem, a parallelogram is given.
It is known that the degree measures of two angles, which are formed with the sides and the diagonal of a given parallelogram, are equal to 28 ° and 68 °, respectively.
Determine how many degrees the first of the angles of the parallelogram is:
28 + 68 = 96 °.
Let’s calculate how many degrees the second angle is, taking into account that the degree measure of all angles in the parallelogram is 360 °.
(360 – 96 * 2) / 2 = (360 – 192) / 2 = 168/2 = 84 °.
Answer: The smaller of the parallelogram angles is 84 °.
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