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Question
the example of finding equal angles.
In the figure above, AB is perpendicular to CD, FD is perpendicular to ED. If angle BDE is 46 degrees, what is the measure of angle ADF in degree?
Solution Method 1
since AB is perpendicular to CD (Given)
so angle CDB = angle CDA = 90o (property of perpendicular lines)
angle CDE = 90o - angle EDB = 90o - 46o = 44o
since FD is perpendicular to ED (Given)
so angle FDE = 90o (property of perpendicular lines)
angle FDC = 90o - angle CDE = 90o - 44o = 46o
since angle CDA = 90o
so angle ADF = 90o - angle FDC = 90o - 46o = 44o
therefore, the degree measure of the angle ADF is 44o
Solution Method 2
since AB is perpendicular to CD (Given)
so angle CDB = angle CDA = 90o
since FD is perpendicular to ED (Given)
so angle FDE = 90o
angle FDA + angle CDF = angle CDF + angle CDE = 90o
so angle FDA = angle CDE = 90o - angle EDB = 90o - 46o = 44o
therefore, the degree measure of the angle FDA is 44o