Question

Quadrilateral LMNO is a rhombus. If the measure of angle LMN is 65 degrees, then what is the measure of angle LMV?

Answer 1

- Before we can find the value of

"The diagonals of a rhombus bisect the opposite angles into two equal angles"

- Thus, with this theorem, we can easily solve the problem as follows:

`\begin{gathered} \angle\text{LMN}=65\degree \\ \text{Diagonal OM bisects }\angle\text{LMN according to the theorem.} \\ \\ \text{Thus, we have that:} \\ \angle\text{LMN}=\angle\text{LMV}+\angle\text{NMV} \\ \text{ Since OM bisects }\angle\text{LMN, we have that} \\ \angle\text{LMV}=\angle\text{NMV} \\ \\ \text{Thus, we can say that} \\ 2\angle\text{LMV}=\angle\text{LMN} \\ \\ \text{But }\angle\text{LMN}=65 \\ \\ 2\angle\text{LMV}=65 \\ \\ \text{Divide both sides by 2} \\ \\ \angle\text{LMV}=(65)/(2)=32.5\degree \end{gathered}`

Final Answer

The measure of