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Geometry
Question
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 = 90
^{o}
(property of perpendicular lines)
angle CDE = 90
^{o}
- angle EDB = 90
^{o}
- 46
^{o}
= 44
^{o}
since FD is perpendicular to ED (Given)
so angle FDE = 90
^{o}
(property of perpendicular lines)
angle FDC = 90
^{o}
- angle CDE = 90
^{o}
- 44
^{o}
= 46
^{o}
since angle CDA = 90
^{o}
so angle ADF = 90
^{o}
- angle FDC = 90
^{o}
- 46
^{o}
= 44
^{o}
therefore, the degree measure of the angle ADF is 44
^{o}
Solution Method 2
since AB is perpendicular to CD (Given)
so angle CDB = angle CDA = 90
^{o}
since FD is perpendicular to ED (Given)
so angle FDE = 90
^{o}
angle FDA +
angle CDF
=
angle CDF
+ angle CDE = 90
^{o}
so angle FDA = angle CDE = 90
^{o}
- angle EDB = 90
^{o}
- 46
^{o}
= 44
^{o}
therefore, the degree measure of the angle FDA is 44
^{o}