Question

In the diagram, $\mathbf{m}\angle \mathbf{VOZ}\mathbf{=}\mathbf{90}$.

$\overline{\mathrm{OW}}$ is an altitude of $△\mathbf{VOZ}$.

$\overline{\mathrm{OX}}$bisects $\angle \mathbf{VOZ}$.

$\overline{\mathrm{OY}}$is a median of $△\mathbf{VOZ}$.

Find the measures of the four numbered angles

$\mathbf{m}\angle \mathbf{Z}\mathbf{=}\mathbf{30}$

Short answer

The measures of the four numbered angles $\angle 1,\angle 2,\angle 3$and $\angle 4$are $30°,15°,15°$and $30°$ respectively.

Step-by-step solution

Step 1. Observe the given diagram.

The given diagram is:

Step 2. Description of step.

It is being given that $m\angle VOZ=90$.

Therefore it can be obtained that:

$\angle 1+\angle 2+\angle 3+\angle 4=90°$.

As, $\overline{OX}$ bisects $\angle VOZ$.

Therefore, $\angle VOZ=2\angle VOX$.

Therefore it can be obtained that:

$\begin{array}{c}\angle VOZ=2\angle VOX\\ 90°=2\angle VOX\\ \frac{90°}{2}=\angle VOX\\ 45°=\angle VOX\end{array}$

Therefore, the measure of the angle $\angle VOX$ is .

As, bisects .

Therefore,

As, , therefore it can be obtained that:

As, , therefore it can be obtained that: