An angle measures \( 146^{\circ} \) less than the measure of its supplementary angle. What is the measure of each angle?

To tackle this angle problem, let's start by recalling that supplementary angles add up to \( 180^{\circ} \). If we let \( x \) represent the measure of the angle in question, then its supplementary angle can be expressed as \( 180^{\circ} - x \). According to the problem, we have: \[ x = (180^{\circ} - x) - 146^{\circ} \] Now, solving for \( x \): 1. Rewrite the equation: \[ x = 180^{\circ} - x - 146^{\circ} \] 2. Combine like terms: \[ x + x = 180^{\circ} - 146^{\circ} \] \[ 2x = 34^{\circ} \] 3. Divide by 2: \[ x = 17^{\circ} \] Now, plug back \( x \) into the expression for the supplementary angle: \[ 180^{\circ} - x = 180^{\circ} - 17^{\circ} = 163^{\circ} \] Thus, the measures of the angles are \( 17^{\circ} \) and \( 163^{\circ} \). The final answer is: The first angle is \( 17^{\circ} \) and the supplementary angle is \( 163^{\circ} \).