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In the given problem, the diagram includes two key pieces of information:

1. \( \triangle UVT \) is an equilateral triangle.
2. \( \angle STU \) is a right angle.

Let's break down the information and solve for \( b \).

### Step 1: Properties of an Equilateral Triangle
Since \( \triangle UVT \) is equilateral, all its angles are equal. The sum of the angles in any triangle is \( 180^\circ \). Therefore, each angle in \( \triangle UVT \) is:
\[
\text{Each angle} = \frac{180^\circ}{3} = 60^\circ
\]
Thus, \( \angle UVT = 60^\circ \).

### Step 2: Use of Right Angle
The problem also states that \( \angle STU \) is a right angle, meaning:
\[
\angle STU = 90^\circ
\]

### Step 3: Relation Between Angles
In \( \triangle STU \), we know that the sum of angles in any triangle is \( 180^\circ \). We already know:
- \( \angle STU = 90^\circ \) (right angle)
- \( \angle UVT = 60^\circ \) (from equilateral triangle)

Therefore, the remaining angle \( b \) (i.e., \( \angle TUS \)) is calculated as:
\[
b = 180^\circ - 90^\circ - 60^\circ = 30^\circ
\]

Thus, \( \angle b = 30^\circ \).

Would you like more details or explanations? Here are 5 related questions to consider:
1. How do we calculate the angles of any polygon using known properties?
2. Why is the sum of the angles in a triangle always \( 180^\circ \)?
3. Can an equilateral triangle ever have a right angle?
4. How does the Pythagorean theorem apply to right triangles?
5. What is the importance of angle properties in geometric constructions?

**Tip**: When solving triangle problems, always double-check the known properties (like whether it's equilateral or isosceles) to simplify angle calculations.

In the diagram below, UVT is an equilateral triangle, and angle STU is a right angle. Calculate the size of angle b.

Solve a geometry problem involving an equilateral triangle and a right-angled triangle. Calculate angle b using triangle angle sum properties. Suitable for students in Grades 8-10.

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