\( \angle 1 \) and \( \angle 2 \) are surphementan angles. If \( m / 1=(2 x-9)^{\circ} \) and \( m / 2=(2 x+21)^{\circ} \), then find the menowe of \( \angle 1 \).

To solve for the measure of \( \angle 1 \), we first need to understand the relationship between supplementary angles. Two angles are supplementary if the sum of their measures equals \( 180^\circ \). Given: - \( m \angle 1 = (2x - 9)^\circ \) - \( m \angle 2 = (2x + 21)^\circ \) Since \( \angle 1 \) and \( \angle 2 \) are supplementary, we can set up the equation: \[ m \angle 1 + m \angle 2 = 180^\circ \] Substituting the expressions for \( m \angle 1 \) and \( m \angle 2 \): \[ (2x - 9) + (2x + 21) = 180 \] Now, let's simplify and solve for \( x \): 1. Combine like terms: \[ 2x - 9 + 2x + 21 = 180 \] \[ 4x + 12 = 180 \] 2. Subtract 12 from both sides: \[ 4x = 180 - 12 \] \[ 4x = 168 \] 3. Divide by 4: \[ x = \frac{168}{4} = 42 \] Now that we have the value of \( x \), we can find the measure of \( \angle 1 \): \[ m \angle 1 = 2x - 9 \] Substituting \( x = 42 \): \[ m \angle 1 = 2(42) - 9 \] \[ m \angle 1 = 84 - 9 \] \[ m \angle 1 = 75^\circ \] Thus, the measure of \( \angle 1 \) is \( 75^\circ \).