In the diagram, \( m \angle A=(4 x-10)^{\circ} \) and \( m \angle D=(2 x+22)^{\circ} \). What is the measure of \( \angle D \) ? (1 point)

To find the measure of angle \( \angle D \), we need to determine the value of \( x \) first. Given that \( m \angle A = (4x - 10)^{\circ} \) and \( m \angle D = (2x + 22)^{\circ} \), we can set up an equation using the fact that the sum of the measures of angles \( \angle A \) and \( \angle D \) is equal to 180 degrees. Let's set up the equation and solve for \( x \) to find the measure of angle \( \angle D \). Solve the equation by following steps: - step0: Solve for \(x\): \(4x-10+2x+22=180\) - step1: Calculate: \(6x+12=180\) - step2: Move the constant to the right side: \(6x=180-12\) - step3: Subtract the numbers: \(6x=168\) - step4: Divide both sides: \(\frac{6x}{6}=\frac{168}{6}\) - step5: Divide the numbers: \(x=28\) The value of \( x \) is 28. Now, we can substitute the value of \( x \) into the expression for the measure of angle \( \angle D \) to find its measure. Substitute \( x = 28 \) into the expression for the measure of angle \( \angle D \): \[ m \angle D = (2x + 22)^{\circ} \] \[ m \angle D = (2(28) + 22)^{\circ} \] \[ m \angle D = (56 + 22)^{\circ} \] \[ m \angle D = 78^{\circ} \] Therefore, the measure of angle \( \angle D \) is \( 78^{\circ} \).