Question

find ( mangle tqw ).
( mangle tqw=square )

Explanation:

Step1: Recall the property of vertical angles

Vertical angles are equal.

Step2: Recall the property of a straight line

The sum of angles on a straight line is \(180^{\circ}\).

Step3: Calculate \(m\angle TQW\)

Since \(m\angle ZQY = m\angle TQW\) (vertical angles), and \(m\angle ZQR=67^{\circ}\), and \(\angle ZQR+\angle ZQY + \angle YQX= 180^{\circ}\), but we can also note that \(\angle ZQR\) and \(\angle TQW\) are supplementary to the same angle formed by the intersection of lines.
\(m\angle TQW=180^{\circ}- 67^{\circ}-67^{\circ}=46^{\circ}\)

Answer:

\(46\)