The height BE is drawn in parallelogram ABCD, and the angle BCD is 4 times the angle ABE. Find the angle ABC.
| September 3, 2021 | education
Let the value of the angle ABE be equal to X0, then, by condition, the angle BCD will be equal to 4 * X0.
Since the parallelogram has opposite angles, the angle BAD = BCD = 4 * X0.
In a right-angled triangle ABE, the sum of the interior angles is 180, then X + 4 * X + 90 = 180.
5 * X = 90.
X = ABE = 90/5 = 180.
The value of the angle ABC = ABE + EBC = 18 + 90 = 108.
Answer: The angle ABE is 108.
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