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H 25° F What is the measure of arc HG? Hint: Remember the measure of the arc is TWICE the measure of the INSCRIBED angle. The INSCRIBED angle is angle HFG. What is the measure of angle HJG? HINT: Remember the measure of the central angle equals the measure of the arc.

H 25° F What is the measure of arc HG? Hint: Remember the measure of the arc is TWICE the measure of the INSCRIBED angle. The INSCRIBED angle is angle HFG. What is the measure of angle HJG? HINT: Remember the measure of the central angle equals the measure of the arc.

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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### Geometry Problems on Circles #### Problem 31 **Diagram Description**: - There is a circle with points \( H \), \( F \), \( J \), and \( G \). - \( H \), \( F \), and \( G \) are points on the circumference, while \( J \) is the center of the circle. - The inscribed angle \( \angle HFG \) measures \( 25^\circ \). **Problem Statement:** What is the measure of arc \( HG \)? **Hint**: Remember the measure of the arc is TWICE the measure of the INSCRIBED angle. The INSCRIBED angle is \( \angle HFG \). **Solution**: The measure of arc \( HG \) is twice the measure of the inscribed angle \( \angle HFG \). Thus, the measure of arc \( HG \) is \( 2 \times 25^\circ = 50^\circ \). --- #### Problem 32 **Problem Statement:** What is the measure of angle \( HJG \)? **Hint**: Remember the measure of the central angle equals the measure of the arc. **Solution**: The measure of the central angle \( \angle HJG \) is equal to the measure of the arc \( HG \). Since the arc \( HG \) measures \( 50^\circ \), \( \angle HJG \) also measures \( 50^\circ \). Diagram explanation for clarification: - The circle portrays an inscribed angle \( \angle HFG \) intersecting arc \( HG \) with \( \angle HFG \) given as \( 25^\circ \). - Central angle \( \angle HJG \) subtends the same arc \( HG \). From the information and hints provided, the following conclusions can be made: - Inscribed angle \( \angle HFG \): \( 25^\circ \). - Corresponding arc \( HG \): \( 50^\circ \) (since it's twice the inscribed angle). - Central angle \( \angle HJG \): \( 50^\circ \) (equal to the measure of arc \( HG \)).
Transcribed Image Text:### Geometry Problems on Circles #### Problem 31 **Diagram Description**: - There is a circle with points \( H \), \( F \), \( J \), and \( G \). - \( H \), \( F \), and \( G \) are points on the circumference, while \( J \) is the center of the circle. - The inscribed angle \( \angle HFG \) measures \( 25^\circ \). **Problem Statement:** What is the measure of arc \( HG \)? **Hint**: Remember the measure of the arc is TWICE the measure of the INSCRIBED angle. The INSCRIBED angle is \( \angle HFG \). **Solution**: The measure of arc \( HG \) is twice the measure of the inscribed angle \( \angle HFG \). Thus, the measure of arc \( HG \) is \( 2 \times 25^\circ = 50^\circ \). --- #### Problem 32 **Problem Statement:** What is the measure of angle \( HJG \)? **Hint**: Remember the measure of the central angle equals the measure of the arc. **Solution**: The measure of the central angle \( \angle HJG \) is equal to the measure of the arc \( HG \). Since the arc \( HG \) measures \( 50^\circ \), \( \angle HJG \) also measures \( 50^\circ \). Diagram explanation for clarification: - The circle portrays an inscribed angle \( \angle HFG \) intersecting arc \( HG \) with \( \angle HFG \) given as \( 25^\circ \). - Central angle \( \angle HJG \) subtends the same arc \( HG \). From the information and hints provided, the following conclusions can be made: - Inscribed angle \( \angle HFG \): \( 25^\circ \). - Corresponding arc \( HG \): \( 50^\circ \) (since it's twice the inscribed angle). - Central angle \( \angle HJG \): \( 50^\circ \) (equal to the measure of arc \( HG \)).
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