https://file.aiquickdraw.com/mathbot/file/1726503081925iswqkh2x.jpg

The question asks to determine the size of angle \( x \) in a quadrilateral. The diagram provided shows that:

- \( AB = AC = AD \) (all sides are equal),
- \( \angle BAD = 90^\circ \),
- \( \angle ABC = 72^\circ \).

### Analyzing the Problem:

1. The triangle \( ABD \) is isosceles since \( AB = AD \), and one of the angles (\( \angle BAD \)) is \( 90^\circ \).
2. The angles in triangle \( ABD \) must sum to \( 180^\circ \). Thus, the sum of the other two angles, \( \angle ABD \) and \( \angle ADB \), must equal \( 90^\circ \). Since the triangle is isosceles, \( \angle ABD = \angle ADB \). Therefore, \( \angle ABD = \angle ADB = \frac{90^\circ}{2} = 45^\circ \).
   
3. Now look at quadrilateral \( ABCD \). The total interior angles of a quadrilateral sum to \( 360^\circ \). Using the known angles:
   - \( \angle BAD = 90^\circ \),
   - \( \angle ABC = 72^\circ \),
   - \( \angle ABD = 45^\circ \).

4. To find \( \angle x \) (or \( \angle ACD \)):
   \[
   \angle x = 360^\circ - (90^\circ + 72^\circ + 45^\circ) = 360^\circ - 207^\circ = 153^\circ.
   \]

Thus, \( \angle x \) should be \( 153^\circ \), **not 72°** as stated in the answer provided in the worksheet.

Let me know if you'd like further details on this or any other questions.

---

Here are five related questions:
1. How do you calculate the sum of angles in any polygon?
2. How do you determine angles in isosceles triangles?
3. What is the significance of the property \( AB = AC = AD \) in this problem?
4. How would the problem change if one of the sides was not equal?
5. What are the key properties of cyclic quadrilaterals?

### Tip:
For any quadrilateral, always remember that the interior angles sum to \( 360^\circ \).

Work out the size of angle x. You must show your working which may be on the diagram.

This problem involves finding angle x in an isosceles quadrilateral with known side lengths and one angle at 90°. The solution uses fundamental geometric principles, such as the sum of angles in quadrilaterals and triangles. Suitable for high school students studying geometry.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation