Question

what is the value of x? 2x + 31°

Explanation:

Step1: Identify the triangle type

Since the two sides of $\triangle TSU$ are equal (marked with crosses), $\triangle TSU$ is an isosceles triangle. In an isosceles triangle, the base - angles are equal. Let the base - angles be $\angle T=\angle U = 2x + 31^{\circ}$. Also, since $TU$ is a diameter of the circle, the angle $\angle S = 90^{\circ}$ (angle inscribed in a semi - circle).

Step2: Use the angle - sum property of a triangle

The sum of the interior angles of a triangle is $180^{\circ}$. So, for $\triangle TSU$, we have $\angle T+\angle U+\angle S=180^{\circ}$. Substituting the values, we get $(2x + 31^{\circ})+(2x + 31^{\circ})+90^{\circ}=180^{\circ}$.

Step3: Simplify the equation

First, combine like terms: $4x+31^{\circ}+31^{\circ}+90^{\circ}=180^{\circ}$, which simplifies to $4x + 152^{\circ}=180^{\circ}$. Then, subtract $152^{\circ}$ from both sides: $4x=180^{\circ}-152^{\circ}$, so $4x = 28^{\circ}$.

Step4: Solve for x

Divide both sides of the equation $4x = 28^{\circ}$ by 4. We get $x=\frac{28^{\circ}}{4}=7^{\circ}$.

Answer:

$7$