Two angles are supplementary. If the first angle is 2 times the second angle, what are the measures of both angles?

Let's denote the first angle as \( A \) and the second angle as \( B \). Given that the two angles are supplementary, we know that their sum is \( 180^\circ \). So, we have: \[ A + B = 180^\circ \] We are also given that the first angle is 2 times the second angle, so we have: \[ A = 2B \] Now we can substitute \( 2B \) for \( A \) in the first equation: \[ 2B + B = 180^\circ \] Combine like terms: \[ 3B = 180^\circ \] Now, divide both sides by 3 to solve for \( B \): \[ B = \frac{180^\circ}{3} \] \[ B = 60^\circ \] Now that we have the measure of the second angle, we can find the measure of the first angle by using the relationship \( A = 2B \): \[ A = 2 \times 60^\circ \] \[ A = 120^\circ \] So, the measures of the two angles are \( 120^\circ \) and \( 60^\circ \).