Question

what is the value of x? 2x - 31° x =

Explanation:

Step1: Recognize isosceles triangle

Since two sides of the triangle in the circle are equal (marked with red - hash), the base - angles of the isosceles triangle are equal. Let the two equal angles be $\angle{I}=\angle{K}=2x - 31^{\circ}$.

Step2: Apply angle - sum property of a triangle

The sum of the interior angles of a triangle is $180^{\circ}$. In $\triangle{IJK}$, if we assume the third angle is $90^{\circ}$ (angle inscribed in a semi - circle is a right angle), then we have the equation $(2x - 31)+(2x - 31)+90 = 180$.

Step3: Simplify the equation

First, combine like terms: $4x-62 + 90=180$, which simplifies to $4x + 28=180$.

Step4: Solve for x

Subtract 28 from both sides: $4x=180 - 28=152$. Then divide both sides by 4: $x=\frac{152}{4}=38$.

Answer:

$38$