The degree measure of the EBC angle is 50º, which is 40% of the ABC angle. The angle DEB is 30% less than the angle EBC. find the degree measure of the angle ABD.
Let’s derive the formula for finding the angle ABD:
From the condition, angle ABC = ABE + DBE + DBC = ABE + EBC (1).
Angle ABD = ABE + DBE (2).
Find the angle ABE from the first equation:
ABE = ABC – EBC.
Substitute this value into equation (2):
ABD = ABE + DBE = ABC – EBC + DBE.
Find the angle ABC and DBE from the conditions.
EBC = 0.4 * ABC.
Therefore, ABC = EBC / 0.4 = 50º / 0.4 = 125º.
The DBE is 100 – 30 = 70% of the EBC.
That is DBE = 0.7 * EBC = 0.7 * 50º = 35º.
Thus, the angle ABD = 125º – 50º + 35º = 110º.
Answer: the angle ABD is 110º.
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