back to *Geometry*
# Example of finding the Equal Angles

- 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}

© Acceler LLC 2022 - www.mathtestpreparation.com