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.