Question

in the figure below, ( mangle 1 = 3x^circ ) and ( mangle 2 = (x + 68)^circ ). find the angle measures. ( mangle 1 = square^circ ) ( mangle 2 = square^circ )

Explanation:

Step1: Identify angle relationship

Angles 1 and 2 form a linear pair, so their sum is \(180^\circ\). Thus, \(3x + (x + 68) = 180\).

Step2: Solve for \(x\)

Simplify the equation: \(4x + 68 = 180\). Subtract 68: \(4x = 112\). Divide by 4: \(x = 28\).

Step3: Find \(m\angle1\)

Substitute \(x = 28\) into \(3x\): \(3(28) = 84\). So \(m\angle1 = 84^\circ\).

Step4: Find \(m\angle2\)

Substitute \(x = 28\) into \(x + 68\): \(28 + 68 = 96\). So \(m\angle2 = 96^\circ\).

Answer:

\(m\angle1 = \boxed{84}^\circ\)
\(m\angle2 = \boxed{96}^\circ\)