Angle Measure Calculation

Setting Up the Supplementary Angle Equation

Let the measure of the unknown angle be $x$.

Two angles are supplementary if their sum is $180^{\circ}$. Therefore, the supplementary angle to $x$ measures $180^{\circ} - x$.

The problem states that the measure of the angle ($x$) is one half of its supplementary angle ($180^{\circ} - x$). This can be written as an equation:

$x = \frac{1}{2} (180^{\circ} - x)$

Solving for the Angle

To find the measure of the angle, we solve the equation:

1. Multiply both sides of the equation by 2 to eliminate the fraction:

   $2 \times x = 2 \times \frac{1}{2} (180^{\circ} - x)$

   $2x = 180^{\circ} - x$

2. Add $x$ to both sides of the equation to gather the terms involving $x$ on one side:

   $2x + x = 180^{\circ} - x + x$

   $3x = 180^{\circ}$

3. Divide both sides by 3 to isolate $x$:

   $x = \frac{180^{\circ}}{3}$

   $x = 60^{\circ}$

Thus, the measure of the angle is $60^{\circ}$.