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# Pls help i dont want just answer pls explain

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In the figure, if the measure of arc  FG is 118 degrees , the measure of arc  FQ is 25 degrees, and FR=FG then what is angle RPG, in degrees?

Thank you in advance, ive been strugling on this problem and i need help and i would really like to understand it. I don't really understand the concept of arcs in general, can you try to explain? Its been very confusing even after being in class

Aug 10, 2024

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To find angle $$RPG$$, we need to use the information given about the arcs and the properties of angles related to them.

1. **Understanding the Arc Measures**:

- The measure of arc $$FG$$ is $$118^\circ$$.

- The measure of arc $$FQ$$ is $$25^\circ$$.

- It is given that $$FR = FG$$, so the measure of arc $$FR$$ is also $$118^\circ$$.

2. **Position of Points**:

- Points $$F, G, R,$$ and $$Q$$ are on a circle. The angles created by the arcs at any point are related to the measure of the arcs intercepted.

- Since $$R$$ is between $$F$$ and $$G$$, we must consider how the angles are formed.

3. **Finding Angle $$RPG$$**:

- Angle $$RPG$$ is the angle formed by the intersection of the lines $$RP$$ and $$RG$$.

- The measure of angle $$RPG$$ will equal half the difference of the measures of the arcs it intercepts. In this case, the relevant arcs are $$FG$$ and $$FQ$$.

Using the formula for the angle:

$\text{Angle} = \frac{1}{2} \left| \text{Arc } FG - \text{Arc } FQ \right|$

we can plug in the arc measures:

$\text{Angle } RPG = \frac{1}{2} \left| 118^\circ - 25^\circ \right| = \frac{1}{2} \left| 93^\circ \right| = \frac{93^\circ}{2} = 46.5^\circ.$

Thus, the measure of angle $$RPG$$ is $$46.5$$ degrees (if we need integer degrees, we might round depending on the context).

Therefore, the final answer is:
$\boxed{46.5}$

degrees.

Aug 10, 2024