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:
- Multiply both sides of the equation by 2 to eliminate the fraction:
$2 \times x = 2 \times \frac{1}{2} (180^{\circ} - x)$
$2x = 180^{\circ} - x$
- Add $x$ to both sides of the equation to gather the terms involving $x$ on one side:
$2x + x = 180^{\circ} - x + x$
$3x = 180^{\circ}$
- Divide both sides by 3 to isolate $x$:
$x = \frac{180^{\circ}}{3}$
$x = 60^{\circ}$
Thus, the measure of the angle is $60^{\circ}$.
Similar Questions
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Important Questions from Lines and Angles
Two parallel lines are intersected by a transversal, the corresponding angles are:
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