ease help with 11

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
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Please help with 11
### Geometry Problem Set

---

#### Problem 10:
**Find the value of \(x\) and \(y\) in the parallelogram.**

**Diagram:**
- A parallelogram with sides labeled as 12, \( y - 9 \), x°, and 7.
- One interior angle is marked as 75°.

---

#### Problem 11:
**Determine the value of \(x\) and \(y\) in the kite.**

**Diagram:**
- A kite diagram with the following annotations:
  - The top and bottom left edges are labeled \(y\).
  - The top right and bottom right edges are labeled \(x\).
  - The left diagonal is labeled 7.5.
  - The right diagonal is labeled 24.
  - The length of the vertical axis of the kite (joining the top and bottom vertices) is labeled 26.

---

### Diagram Explanation for Problem 11:

The kite is a quadrilateral with:
- Two pairs of adjacent sides equal. The pairs \(y\), \(y\) and \(x\), \(x\).
- The diagonals intersecting at a right angle.
- The lengths of the diagonals are 7.5 and 24 respectively, meeting at the center to form triangles.

To solve for \(x\) and \(y\), use the Pythagorean theorem in the triangles formed by the diagonals. This involves finding the median of 7.5 and 24, which intersect to form the right angle, and using it with the entire length of 26 to form two main triangles sharing that height.
Transcribed Image Text:### Geometry Problem Set --- #### Problem 10: **Find the value of \(x\) and \(y\) in the parallelogram.** **Diagram:** - A parallelogram with sides labeled as 12, \( y - 9 \), x°, and 7. - One interior angle is marked as 75°. --- #### Problem 11: **Determine the value of \(x\) and \(y\) in the kite.** **Diagram:** - A kite diagram with the following annotations: - The top and bottom left edges are labeled \(y\). - The top right and bottom right edges are labeled \(x\). - The left diagonal is labeled 7.5. - The right diagonal is labeled 24. - The length of the vertical axis of the kite (joining the top and bottom vertices) is labeled 26. --- ### Diagram Explanation for Problem 11: The kite is a quadrilateral with: - Two pairs of adjacent sides equal. The pairs \(y\), \(y\) and \(x\), \(x\). - The diagonals intersecting at a right angle. - The lengths of the diagonals are 7.5 and 24 respectively, meeting at the center to form triangles. To solve for \(x\) and \(y\), use the Pythagorean theorem in the triangles formed by the diagonals. This involves finding the median of 7.5 and 24, which intersect to form the right angle, and using it with the entire length of 26 to form two main triangles sharing that height.
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