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NOPQ is a rhombus. Given ON = 110 and OQ = 176. Find each measures. 16) m40PN = 17) m*NOQ = 19) m40PQ = = 21) m42 =_ 23) m44 = 25) OR = 27) NR = 18) m*NQP = 20) mx1 = 22) m43 = 24) OP=_ 26) NP = ( 110 110 64% N R 3

NOPQ is a rhombus. Given ON = 110 and OQ = 176. Find each measures. 16) m40PN = 17) m*NOQ = 19) m40PQ = = 21) m42 =_ 23) m44 = 25) OR = 27) NR = 18) m*NQP = 20) mx1 = 22) m43 = 24) OP=_ 26) NP = ( 110 110 64% N R 3

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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### Educational Content on Geometry: Rhombi and Heptagons #### Exercises: **Geometry Problems:** **NOPQ is a rhombus.** Given \(ON = 110\) and \(OQ = 176\). Find each measurement: 1. \(m \angle OPN =\) _______ 2. \(m \angle NOQ =\) _______ 3. \(m \angle NQP =\) _______ 4. \(m \angle OPQ =\) _______ 5. \(m \angle 1 =\) _______ 6. \(m \angle 2 =\) _______ 7. \(m \angle 3 =\) _______ 8. \(m \angle 4 =\) _______ 9. \(OP =\) _______ 10. \(OR =\) _______ 11. \(NP =\) _______ 12. \(NR =\) _______ **Diagram Explanation:** In the diagram of the rhombus \(NOPQ\), with \(O\) at the center, \(N\) and \(Q\) are opposite vertices. Lines and angles are marked as follows: - \(ON\) and \(OQ\) are radii of the rhombus, measuring 110 and 176, respectively. - The angles \( \angle OPN\), \( \angle NOQ\), etc., are marked, denoting different regions within the rhombus. - An angle of 64° is specifically marked near \( \angle 3\). **Additional Task:** 28. **Find the interior angle sum and exterior angle sum for a heptagon.** **Diagram of Heptagon:** A simple heptagon is drawn with each side representing one of its 7 edges. ### Concepts to Explore: - **Rhombus Properties:** - All sides are equal. - Opposite angles are equal. - The diagonals bisect each other at right angles. - **Heptagon Angle Sums:** - Interior angle sum: \((n-2) \times 180^\circ\) where \(n = 7\). - Exterior angle sum is always \(360^\circ\) for any polygon. These exercises provide practice with understanding the properties of rhombi and polygons, important for strengthening geometric reasoning and problem-solving skills.
Transcribed Image Text:### Educational Content on Geometry: Rhombi and Heptagons #### Exercises: **Geometry Problems:** **NOPQ is a rhombus.** Given \(ON = 110\) and \(OQ = 176\). Find each measurement: 1. \(m \angle OPN =\) _______ 2. \(m \angle NOQ =\) _______ 3. \(m \angle NQP =\) _______ 4. \(m \angle OPQ =\) _______ 5. \(m \angle 1 =\) _______ 6. \(m \angle 2 =\) _______ 7. \(m \angle 3 =\) _______ 8. \(m \angle 4 =\) _______ 9. \(OP =\) _______ 10. \(OR =\) _______ 11. \(NP =\) _______ 12. \(NR =\) _______ **Diagram Explanation:** In the diagram of the rhombus \(NOPQ\), with \(O\) at the center, \(N\) and \(Q\) are opposite vertices. Lines and angles are marked as follows: - \(ON\) and \(OQ\) are radii of the rhombus, measuring 110 and 176, respectively. - The angles \( \angle OPN\), \( \angle NOQ\), etc., are marked, denoting different regions within the rhombus. - An angle of 64° is specifically marked near \( \angle 3\). **Additional Task:** 28. **Find the interior angle sum and exterior angle sum for a heptagon.** **Diagram of Heptagon:** A simple heptagon is drawn with each side representing one of its 7 edges. ### Concepts to Explore: - **Rhombus Properties:** - All sides are equal. - Opposite angles are equal. - The diagonals bisect each other at right angles. - **Heptagon Angle Sums:** - Interior angle sum: \((n-2) \times 180^\circ\) where \(n = 7\). - Exterior angle sum is always \(360^\circ\) for any polygon. These exercises provide practice with understanding the properties of rhombi and polygons, important for strengthening geometric reasoning and problem-solving skills.
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