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### Educational Resource - Geometry Problem Solving #### Instructions: Use the diagram (not drawn to scale) and the given information. **Diagram Description:** - A circle is shown with points A, B, C, D, E, F, G, H, and P marked around it. - Point A is on the circumference of the circle, while point P is outside the circle. - A line extends from P to H passing through A and intersecting the circle at points B and C. - Another line extends from A to intersect points D and E on the circle. - Additional points F and G are marked on the circle connecting other parts of the diagram. #### Problems: **16.** Given: - \( m\angle BCD = 114^\circ \) - \( m\angle DEF = 94^\circ \) - \( m\angle FGH = 136^\circ \) - \( m\angle HAB = 16^\circ \) Find \( m\angle FPD \). Options: a. \( 39^\circ \) b. \( 21^\circ \) c. \( 16^\circ \) d. \( 98^\circ \) **17.** Given: - \( m\angle BCD = 111^\circ \) - \( m\angle DEF = 100^\circ \) - \( m\angle FGH = 127^\circ \) - \( m\angle HAB = 22^\circ \) Find \( m\angle FPD \). #### Circle Geometry: This problem involves the use of various circle theorems and properties, including: - Angles at the center and circumference - Angle properties in cyclic quadrilaterals - Exterior angles of a circle By applying these properties and calculating appropriately, the correct angles can be determined. Remember to review the corresponding geometric theorems and use accurate calculation methods to solve the problems provided.

### Educational Resource - Geometry Problem Solving #### Instructions: Use the diagram (not drawn to scale) and the given information. **Diagram Description:** - A circle is shown with points A, B, C, D, E, F, G, H, and P marked around it. - Point A is on the circumference of the circle, while point P is outside the circle. - A line extends from P to H passing through A and intersecting the circle at points B and C. - Another line extends from A to intersect points D and E on the circle. - Additional points F and G are marked on the circle connecting other parts of the diagram. #### Problems: **16.** Given: - \( m\angle BCD = 114^\circ \) - \( m\angle DEF = 94^\circ \) - \( m\angle FGH = 136^\circ \) - \( m\angle HAB = 16^\circ \) Find \( m\angle FPD \). Options: a. \( 39^\circ \) b. \( 21^\circ \) c. \( 16^\circ \) d. \( 98^\circ \) **17.** Given: - \( m\angle BCD = 111^\circ \) - \( m\angle DEF = 100^\circ \) - \( m\angle FGH = 127^\circ \) - \( m\angle HAB = 22^\circ \) Find \( m\angle FPD \). #### Circle Geometry: This problem involves the use of various circle theorems and properties, including: - Angles at the center and circumference - Angle properties in cyclic quadrilaterals - Exterior angles of a circle By applying these properties and calculating appropriately, the correct angles can be determined. Remember to review the corresponding geometric theorems and use accurate calculation methods to solve the problems provided.

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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### Educational Resource - Geometry Problem Solving #### Instructions: Use the diagram (not drawn to scale) and the given information. **Diagram Description:** - A circle is shown with points A, B, C, D, E, F, G, H, and P marked around it. - Point A is on the circumference of the circle, while point P is outside the circle. - A line extends from P to H passing through A and intersecting the circle at points B and C. - Another line extends from A to intersect points D and E on the circle. - Additional points F and G are marked on the circle connecting other parts of the diagram. #### Problems: **16.** Given: - \( m\angle BCD = 114^\circ \) - \( m\angle DEF = 94^\circ \) - \( m\angle FGH = 136^\circ \) - \( m\angle HAB = 16^\circ \) Find \( m\angle FPD \). Options: a. \( 39^\circ \) b. \( 21^\circ \) c. \( 16^\circ \) d. \( 98^\circ \) **17.** Given: - \( m\angle BCD = 111^\circ \) - \( m\angle DEF = 100^\circ \) - \( m\angle FGH = 127^\circ \) - \( m\angle HAB = 22^\circ \) Find \( m\angle FPD \). #### Circle Geometry: This problem involves the use of various circle theorems and properties, including: - Angles at the center and circumference - Angle properties in cyclic quadrilaterals - Exterior angles of a circle By applying these properties and calculating appropriately, the correct angles can be determined. Remember to review the corresponding geometric theorems and use accurate calculation methods to solve the problems provided.
Transcribed Image Text:### Educational Resource - Geometry Problem Solving #### Instructions: Use the diagram (not drawn to scale) and the given information. **Diagram Description:** - A circle is shown with points A, B, C, D, E, F, G, H, and P marked around it. - Point A is on the circumference of the circle, while point P is outside the circle. - A line extends from P to H passing through A and intersecting the circle at points B and C. - Another line extends from A to intersect points D and E on the circle. - Additional points F and G are marked on the circle connecting other parts of the diagram. #### Problems: **16.** Given: - \( m\angle BCD = 114^\circ \) - \( m\angle DEF = 94^\circ \) - \( m\angle FGH = 136^\circ \) - \( m\angle HAB = 16^\circ \) Find \( m\angle FPD \). Options: a. \( 39^\circ \) b. \( 21^\circ \) c. \( 16^\circ \) d. \( 98^\circ \) **17.** Given: - \( m\angle BCD = 111^\circ \) - \( m\angle DEF = 100^\circ \) - \( m\angle FGH = 127^\circ \) - \( m\angle HAB = 22^\circ \) Find \( m\angle FPD \). #### Circle Geometry: This problem involves the use of various circle theorems and properties, including: - Angles at the center and circumference - Angle properties in cyclic quadrilaterals - Exterior angles of a circle By applying these properties and calculating appropriately, the correct angles can be determined. Remember to review the corresponding geometric theorems and use accurate calculation methods to solve the problems provided.
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