Question

09/17 - angles quiz l
\\(\overrightarrow{pc}\\) bisects \\(\angle bpd\\).
if \\(m\angle cpd = 28^{circ}\\), then \\(m\angle bpc=)
if \\(m\angle dpb = 62^{circ}\\), then \\(m\angle dpc=)

Explanation:

Step1: Recall angle - bisector property

An angle - bisector divides an angle into two equal angles. So if $\overrightarrow{PC}$ bisects $\angle BPD$, then $\angle BPC=\angle CPD$.

Step2: Solve the first part

Given $m\angle CPD = 28^{\circ}$, since $\angle BPC=\angle CPD$, then $m\angle BPC = 28^{\circ}$.

Step3: Solve the second part

Given $m\angle DPB=62^{\circ}$, and since $\overrightarrow{PC}$ bisects $\angle BPD$, then $m\angle DPC=\frac{1}{2}m\angle DPB$. So $m\angle DPC=\frac{1}{2}\times62^{\circ}=31^{\circ}$.

Answer:

$28$
$31$