Maria constructed the angle bisector of angle ABC by constructing ray BD. Maria then constructed the angle bisector of DBC by constructing ray BE. If the measurement of angle ABC is 68 degrees, what is the measurement of angle EBC?

Answer 1

To find the measurement of angle EBC, we start with the given angle ABC, which measures 68 degrees.

1. Maria constructs the angle bisector BD of angle ABC. Since BD is an angle bisector, it divides angle ABC into two equal angles: \[ \angle ABD = \angle DBC = \frac{68^\circ}{2} = 34^\circ \]

2. Next, Maria constructs ray BE, which is the angle bisector of angle DBC. Since DBC measures 34 degrees, ray BE will also divide this angle into two equal parts: \[ \angle ABE = \angle EBC = \frac{34^\circ}{2} = 17^\circ \]

Thus, the measurement of angle EBC is \( \boxed{17} \) degrees.