Question

given that \\( \overline { a b } \parallel \overline { d c } \\), \\( m \angle 1 = 112 \\), \\( m \angle 2 = 4 x \\), and \\( m \angle 3 = 3 x + 12 \\), find \\( m \angle d \\). after you enter your answer press go. \\( m \angle d = \\)

Explanation:

Step1: Find the value of \(x\)

Since \(\overline{AB}\parallel\overline{DC}\), \(\angle1+\angle D = 180^{\circ}\) (same - side interior angles). Also, \(\angle2=\angle3\) (alternate interior angles).
Set \(4x = 3x + 12\).
Subtract \(3x\) from both sides: \(4x-3x=3x + 12-3x\), so \(x = 12\).

Step2: Calculate \(m\angle2\)

Substitute \(x = 12\) into \(m\angle2=4x\). Then \(m\angle2=4\times12 = 48^{\circ}\).

Step3: Calculate \(m\angle D\)

Since \(\angle1+\angle D = 180^{\circ}\), and \(m\angle1 = 112^{\circ}\), then \(m\angle D=180 - 112=68^{\circ}\).

Answer:

\(68\)