The acute angle of the parallelogram is 30 degrees less than the obtuse angle. Find the angles of a parallelogram.
| January 4, 2021 | education
Parallelogram – quadrangle
The sum of the angles of any convex quadrilateral is 360 °
By the definition of a parallelogram, opposite angles are pairwise equal
Let x be a smaller angle, then a larger x + 30 °
2x + 2 (x + 30) = 360
2x + 2x + 60 = 360
4x = 300
x = 75 (°) smaller angle
Then the greater 75 ° + 30 ° = 105 °
Answer: smaller angle 75 °, larger angle 105 °
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