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Solve straight i don't wat long explanation pls

To solve for the angle \( \angle EFG \):

- We know that \( \angle EGH = 48^\circ \) and \( \angle OHG = 31^\circ \).
- Notice that \( \triangle EFG \) is inscribed in the circle.

By the **Angle at the Center Theorem**, the angle subtended by a chord at the center of the circle (here, \( \angle EOF \)) is twice the angle subtended at the circumference on the same side (i.e., \( \angle EFG \)).

Thus, 
\[
\angle EFG = \frac{1}{2} \times \angle EOH
\]

Since \( \angle EOH = 31^\circ + 48^\circ = 79^\circ \) (angle sum at the center),
\[
\angle EFG = \frac{1}{2} \times 79^\circ = 39.5^\circ.
\]

The size of \( \angle EFG = 39.5^\circ \).

Would you like more details or have any questions?

Here are 5 related questions:
1. How does the Angle at the Center Theorem apply in different circle problems?
2. What is the significance of inscribed angles in a circle?
3. How would the solution change if \( \angle OHG \) were different?
4. Can the Angle at the Center Theorem be used for angles outside the circle?
5. What are the properties of cyclic quadrilaterals in circles?

**Tip**: The sum of angles in any triangle always equals 180 degrees; this is useful in many geometric problems!

Work out the size of angle EFG in the given circle. Points E, F, G, and H are on the circumference, and you are given angles CHG = 31° and EGH = 48°.

This geometry problem focuses on finding the size of angle EFG in a circle using the Angle at the Center Theorem. Given angles CHG = 31° and EGH = 48°, learn how to apply key circle theorems to solve for unknown angles.

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