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### Q.8: 
**Question:** If the angles of a quadrilateral are 90°, 7x – 30°, 2x – 30°, and 2x, find the greatest angle.

**Solution:**
1. The sum of the angles in a quadrilateral is always 360°.
   
   Therefore, we have:
   \[
   90 + (7x - 30) + (2x - 30) + 2x = 360
   \]

2. Combine like terms:
   \[
   90 + 7x - 30 + 2x - 30 + 2x = 360
   \]
   \[
   90 - 30 - 30 + 11x = 360
   \]
   \[
   30 + 11x = 360
   \]

3. Subtract 30 from both sides:
   \[
   11x = 330
   \]

4. Solve for \( x \):
   \[
   x = 30
   \]

5. Substitute \( x = 30 \) back into the expressions for the angles:
   - \( 7x - 30 = 7(30) - 30 = 210 - 30 = 180 \)
   - \( 2x - 30 = 2(30) - 30 = 60 - 30 = 30 \)
   - \( 2x = 2(30) = 60 \)

   Therefore, the angles are 90°, 180°, 30°, and 60°.

6. **Greatest angle:** 180°.

---

### Q.9: 
**Question:** The angles of a quadrilateral are in the ratio 1:3:4:7. Find the difference between the largest and smallest.

**Solution:**
1. Let the angles be \( x \), \( 3x \), \( 4x \), and \( 7x \).

2. The sum of the angles in a quadrilateral is 360°:
   \[
   x + 3x + 4x + 7x = 360
   \]
   \[
   15x = 360
   \]

3. Solve for \( x \):
   \[
   x = 24
   \]

4. Therefore, the angles are:
   - \( x = 24° \)
   - \( 3x = 72° \)
   - \( 4x = 96° \)
   - \( 7x = 168° \)

5. **Difference between the largest and smallest angles:** 
   \[
   168° - 24° = 144°
   \]

---

### Q.10: 
**Question:** If the angles are \( 3x + 21 \) and \( 5x - 41 \), find the measure of the smallest angle.

**Solution:**
1. The two given expressions represent angles. Let's solve for \( x \) assuming they add up to 180° (if they are supplementary):
   \[
   (3x + 21) + (5x - 41) = 180
   \]

2. Simplify:
   \[
   3x + 21 + 5x - 41 = 180
   \]
   \[
   8x - 20 = 180
   \]

3. Add 20 to both sides:
   \[
   8x = 200
   \]

4. Solve for \( x \):
   \[
   x = 25
   \]

5. Substitute \( x = 25 \) into the angles:
   - \( 3x + 21 = 3(25) + 21 = 75 + 21 = 96° \)
   - \( 5x - 41 = 5(25) - 41 = 125 - 41 = 84° \)

6. **Smallest angle:** 84°.

---

### Q.11:
**Question:** If adjacent sides of a parallelogram are equal, then the parallelogram is:
   1. Rectangle
   2. Trapezium
   3. Rhombus
   4. All of the above

**Answer:** A parallelogram with adjacent sides equal is a **Rhombus** (Option 3).

---

### Q.12: 
**Question:** Name the quadrilateral whose diagonals and angles are equal.

**Answer:** The quadrilateral with both equal diagonals and equal angles is a **Square**.

---

### Q.13: 
**Question:** Which of the following figures satisfies any of these properties:
   1. All sides are equal.
   2. All angles are right angles.
   3. Opposite sides are parallel.

This appears to be a multiple-choice question with diagrams labeled P, Q, R, S. Without the diagram, I cannot answer it fully, but likely options would correspond to familiar shapes like squares, rectangles, rhombuses, etc.

---

Would you like to go into further detail about any of these? Here are some related questions you might find interesting:

1. What is the total sum of the internal angles for any polygon?
2. How do you prove that a parallelogram with equal adjacent sides is a rhombus?
3. How are the diagonals of a rhombus different from those of a square?
4. What is the formula for the sum of angles in any polygon?
5. How do you classify quadrilaterals based on angle and side properties?

**Tip:** When solving for angles in polygons, always check the sum of the angles (e.g., 180° for a triangle, 360° for a quadrilateral).

If the angles of quadrilateral are 90°, 7x - 30°, 2x - 30°, and 2x, find the greatest angle. The angles of quadrilateral are in ratio 1:3:4:7, find the difference between largest and smallest. 3x + 21 and 5x - 41, find the measure of smallest angle. If adjacent parallelograms are equal then parallelogram is a: 1. Rectangle, 2. Trapezium, 3. Rhombus, 4. All of the above. Name the quadrilateral whose diagonals and angles are equal. Which of the following figures satisfies any of these properties: 1. All sides are equal, 2. All angles are right angles, 3. Opposite sides are parallel.

Solve a series of problems involving quadrilaterals, including finding the greatest angle, comparing angles in ratio, identifying properties of parallelograms, and more. This page covers key algebraic and geometric concepts, suitable for students in Grades 7-9.

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