Question

the measure of an angle is 34°. what is the measure of its supplement? 34° 56° 146° 214°

Explanation:

Step1: Recall the definition of supplementary angles

Supplementary angles are two angles whose sum is \(180^\circ\). Let the measure of the given angle be \(x = 34^\circ\) and the measure of its supplement be \(y\). Then we have the equation \(x + y=180^\circ\).

Step2: Solve for the supplement

Substitute \(x = 34^\circ\) into the equation \(34^\circ+y = 180^\circ\). To find \(y\), we subtract \(34^\circ\) from both sides of the equation: \(y=180^\circ - 34^\circ\). Calculating the right - hand side, \(180 - 34=146\), so \(y = 146^\circ\).

Answer:

\(146^\circ\) (corresponding to the option with \(146^\circ\))