Question

which of the following statements is true? answer $\frac{1}{2}(mangle cdf)=mangle edf$ $mangle cde = mangle edf$ $mangle cde = 2(mangle edf)$ $mangle cdf=\frac{1}{2}(mangle edf)$

Explanation:

Step1: Observe angle - bisector property

If a ray $DE$ bisects $\angle CDF$, then by the definition of an angle - bisector, it divides the angle $\angle CDF$ into two equal angles. That is, $m\angle CDE = m\angle EDF$ and $m\angle CDF=m\angle CDE + m\angle EDF$. Since $m\angle CDE = m\angle EDF$, we can substitute $m\angle CDE$ with $m\angle EDF$ in the equation $m\angle CDF=m\angle CDE + m\angle EDF$. So $m\angle CDF = 2m\angle EDF$, which is equivalent to $\frac{1}{2}(m\angle CDF)=m\angle EDF$.

Answer:

A. $\frac{1}{2}(m\angle CDF)=m\angle EDF$