https://file.aiquickdraw.com/mathbot/file/1726890672964ofjkn7fr.jpg

The question in the image asks to calculate several angles in a cyclic quadrilateral \( DEFG \) inscribed in a circle. 

### Given:
- \( \angle GFH = 95^\circ \)
- \( \angle G = 73^\circ \)

### Cyclic Quadrilateral Properties:
In a cyclic quadrilateral, opposite angles are supplementary, meaning their sum is \( 180^\circ \).

#### a. Finding \( \angle EFG \):
Using the property that \( \angle G + \angle EFG = 180^\circ \) (since \( G \) and \( EFG \) are opposite angles in the quadrilateral):
\[
\angle EFG = 180^\circ - \angle G = 180^\circ - 73^\circ = 107^\circ
\]

#### b. Finding \( \angle D \):
Since \( DEFG \) is a cyclic quadrilateral, \( \angle GFH \) and \( \angle D \) are opposite. Thus:
\[
\angle D = 180^\circ - \angle GFH = 180^\circ - 95^\circ = 85^\circ
\]

#### c. Finding \( \angle E \):
Using the supplementary property for \( \angle E \) and \( \angle F \) (which is calculated as \( \angle EFG \)):
\[
\angle E = 180^\circ - \angle EFG = 180^\circ - 107^\circ = 73^\circ
\]

### Final Answers:
- \( \angle EFG = 107^\circ \)
- \( \angle D = 85^\circ \)
- \( \angle E = 73^\circ \)

Would you like further details or explanations? 

Here are five related questions you might find helpful:
1. What are the properties of angles in a cyclic quadrilateral?
2. How can you determine if a quadrilateral is cyclic?
3. What is the relationship between the opposite angles of a cyclic quadrilateral?
4. Can a non-cyclic quadrilateral inscribed in a circle have the same angle properties?
5. How do inscribed angles relate to the intercepted arc in a circle?

**Tip:** Always remember that the sum of opposite angles in a cyclic quadrilateral is \(180^\circ\).

Pada gambar berikut, DEFG adalah segi empat busur. Besar ∠GFH = 95° dan ∠G = 73°. Hitunglah: a) Besar ∠EFG b) Besar ∠D c) Besar ∠E

Solve for the angles ∠EFG, ∠D, and ∠E in the cyclic quadrilateral DEFG inscribed in a circle. Using properties of cyclic quadrilaterals, this problem demonstrates how opposite angles are supplementary. The given values are ∠GFH = 95° and ∠G = 73°.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation