Chapter 6, Problem 14CT

To determine

To prove: t $\text{he largest angle}$ of $\text{ΔUVE}$ , with the help of given information.

Answer to Problem 14CT

  $\text{The the largest angle of ΔUVE is }\angle EUV.$

Explanation of Solution

Given information:

The system information is:

  $m\angle EVU=60,\overline{OE}\cong \overline{OU}\text{ and }m\angle VOE>m\angle VOU$

Proof:

Consider the figure provided in the textbook

Also consider that

If $m\angle EVU=60,\overline{OE}\cong \overline{OU},m\angle VOE>m\angle VOU$

Find the largest angle of $\text{Δ}$

UVE as follows:

In triangles, the segment opposite the larger angle is greater than the segment opposite the smaller angle.

Look at $△\text{sVOU}$ and $\text{VOE},$ since $\text{m}\angle \text{VOE}>\text{m}\angle \text{VOU},VE>\text{VU}$

  $\begin{array}{l}\text{Therefore, }\angle VUE>\angle VEU\\ \text{As in Δ}VEU,EU\text{ cannot be greater than }VE\text{ as }EU\text{ is in the bigger Δ}VEO\text{.}\\ \text{Hence, }\angle EUV>\angle EVU\end{array}$

  $\text{Hence, in ΔUVE, the largest angle is }\angle EUV$