Question

In the figure, DA FB and EC are parallel lines and t is a transversal perpendicular to DA. FB is the bisector of angle DEF. If angle DFE=82, find angle ADF, CEF, FBC, and BCE?

Answer 1

Angle ADF = 82 degrees, Angle CEF = 82 degrees, Angle FBC = 98 degrees, and Angle BCE = 98 degrees.

Explanation:

In the given figure, DA || FB and EC, and t is a transversal perpendicular to DA. Since FB is the bisector of angle DEF, it divides angle DFE into two equal parts. Given that angle DFE is 82 degrees, the bisector FB splits it into two angles of 41 degrees each. Therefore, angle ADF and angle CEF are both 82 degrees.

Now, considering the alternate interior angles formed by the parallel lines DA, FB, and EC, angle FBC is equal to angle DFE, which is 82 degrees. Similarly, angle BCE is equal to angle FED, and both are also 82 degrees.

In summary, angle ADF and angle CEF are 82 degrees each, while angle FBC and angle BCE are both 98 degrees each. These angle measures are a result of the given geometric relationships within the parallel lines and transversal configuration.