https://file.aiquickdraw.com/mathbot/file/1728507299152xh9e5dqq.jpg

Let's analyze the image.

### Part (a):
The quadrilateral has two pairs of adjacent sides that are equal in length, suggesting it resembles a **kite**. In a kite, two pairs of adjacent sides are equal, and there is symmetry along one diagonal.

Thus, the answer to part (a) is **Kite**.

---

### Part (b):
To find the size of angle \( y \), we use the fact that the sum of interior angles in any quadrilateral is always 360°. The given angles are:

- \( 96^\circ \)
- \( 51^\circ \)
- \(  y^\circ \)
- The fourth angle (which I will call \( x \)) is vertically opposite to the \( 96^\circ \) angle, so it is also \( 96^\circ \).

We can now set up the equation:
\[
96^\circ + 51^\circ + 96^\circ + y = 360^\circ
\]
Simplifying:
\[
243^\circ + y = 360^\circ
\]
\[
y = 360^\circ - 243^\circ
\]
\[
y = 117^\circ
\]

Thus, the size of angle \( y \) is \( \boxed{117^\circ} \).

---

Would you like more details or have any further questions?

### Related Questions:
1. What is the sum of interior angles for any polygon?
2. Can a trapezium ever have the properties of a kite?
3. How do you classify quadrilaterals based on side length and angle properties?
4. What are the distinguishing features of a rhombus compared to a kite?
5. In a kite, how are the diagonals related?

### Tip:
In any polygon, always remember that the sum of the interior angles is given by the formula \((n-2) \times 180^\circ\), where \(n\) is the number of sides. For a quadrilateral, this is always 360°.

A quadrilateral is shown with specific angles, and the tasks are to (a) identify the type of quadrilateral, and (b) calculate the size of a missing angle.

This problem involves classifying a quadrilateral as a kite based on its properties and calculating a missing angle using the sum of interior angles in a quadrilateral. It is suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation