Question

Прямі АВ і РК перпендикулярні., точка О - точка їх перетину. Промінь ОМ ділить кут КОВ навпіл. Знайдіть величину кута МОВ.

Answer 1

I can help you with your math problem. Here is a detailed solution:

Since AB and RK are perpendicular, we know that $$\angle AOR = \angle ROK = 90^\circ$$

Since OM bisects $$\angle KOV$$, we know that $$\angle KOM = \angle MOV$$

We can use the angle sum property of a triangle to find $$\angle KOM$$ and $$\angle MOV$$:

$$\angle KOM + \angle KMO + \angle MOK = 180^\circ$$ $$\angle MOV + \angle MOA + \angle AOV = 180^\circ$$

Substituting $$\angle KMO = \angle MOA = 90^\circ$$ and $$\angle KOM = \angle MOV$$, we get:

$$2\angle KOM + 90^\circ = 180^\circ$$ $$\angle KOM = \angle MOV = \frac{180^\circ - 90^\circ}{2} = 45^\circ$$

Therefore, the measure of $$\angle MOV$$ is $$45^\circ$$.

I hope this helps. If you have any other questions, feel free to ask me.