Question

∠ber≅∠ceu
given: m∠ber = 40°
m∠rec = 125°
m∠web = ____
find: m∠reu = ____
m∠wer = ____

Explanation:

Step1: Find $m\angle WEB$

Since $\angle WEB$ and $\angle BEC$ are supplementary (a straight - line angle is $180^{\circ}$) and $\angle BEC=\angle BER + \angle REC$. Given $\angle BER = 40^{\circ}$ and $\angle REC=125^{\circ}$, then $\angle BEC=40^{\circ}+125^{\circ}=165^{\circ}$. So $m\angle WEB = 180^{\circ}-165^{\circ}=15^{\circ}$.

Step2: Find $m\angle REU$

Given $\angle BER\cong\angle CEU$ and $m\angle BER = 40^{\circ}$, so $m\angle CEU = 40^{\circ}$. And since $\angle REC = 125^{\circ}$, then $m\angle REU=m\angle REC - m\angle CEU=125^{\circ}-40^{\circ}=85^{\circ}$.

Step3: Find $m\angle WER$

$\angle WER$ and $\angle REC$ are supplementary. So $m\angle WER = 180^{\circ}-m\angle REC=180^{\circ}-125^{\circ}=55^{\circ}$.

Answer:

$m\angle WEB = 15^{\circ}$
$m\angle REU = 85^{\circ}$
$m\angle WER = 55^{\circ}$