Question

find ( mangle tqw ).
( mangle tqw=square^{circ} )

Explanation:

Step1: Recall the property of a straight - line angle

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

Step2: Set up the equation

We know that \(\angle RQY+\angle YQW+\angle TQW = 180^{\circ}\). But \(\angle RQY = 67^{\circ}\) and \(\angle YQW\) and \(\angle ZQR\) are vertical angles. Since \(\angle ZQR = 67^{\circ}\), then \(\angle YQW=67^{\circ}\) (vertical angles are equal). Let \(m\angle TQW=x\). So, \(67^{\circ}+67^{\circ}+x = 180^{\circ}\).

Step3: Solve for \(x\)

First, simplify the left - hand side of the equation: \(134^{\circ}+x = 180^{\circ}\). Then, subtract \(134^{\circ}\) from both sides: \(x=180^{\circ}-134^{\circ}\). So, \(x = 46^{\circ}\).

Answer:

\(46\)