If the blue angle measures MEASURE degrees, what does the orange angle measure?
This is a special case where the blue and orange angles' sides share the same line. The blue angle is called a central angle, and the orange angle is called an inscribed angle.
The green and blue angles are supplementary. Because the blue angle is MEASURE degrees, the green angle must be 180 - MEASURE degrees.
We know that the angles in a triangle sum to 180 degrees.
\color{GREEN}{\text{green angle}} + \color{PINK}{\text{pink angle}} + \color{ORANGE}{\text{orange angle}} = 180^{\circ}
The pink sides of the triangle are radii, so they must be equal.
This means that the triangle is isosceles and that the base angles, or the pink and orange angles, are equal.
\color{GREEN}{\text{green angle}} + 2 \cdot \color{ORANGE}{\text{orange angle}} = 180^{\circ}
2 \cdot \color{ORANGE}{\text{orange angle}} = 180^{\circ} - \color{GREEN}{180 - MEASURE^{\circ}}
2 \cdot \color{ORANGE}{\text{orange angle}} = \color{BLUE}{MEASURE^{\circ}}
\color{ORANGE}{\text{orange angle}} = \dfrac{1}{2} \cdot \color{BLUE}{MEASURE^{\circ}}
\color{ORANGE}{\text{orange angle}} = \color{BLUE}{MEASURE / 2^{\circ}}