Question

find m∠tqw. m∠tqw=?

Explanation:

Step1: Recall the property of a straight - line angle

A straight - line angle is \(180^{\circ}\). The angles \(\angle RQZ\), \(\angle ZQT\), \(\angle TQW\), and \(\angle WQX\) around point \(Q\) on the line \(RX\) form a straight - line angle. Also, \(\angle RQZ=\angle WQX = 67^{\circ}\) (vertically opposite angles are equal).

Step2: Set up the equation

Let \(m\angle TQW=x\). Then \(67^{\circ}+67^{\circ}+x = 180^{\circ}\) (since \(\angle RQZ+\angle ZQT+\angle TQW+\angle WQX = 180^{\circ}\) and \(\angle ZQT\) and \(\angle WQX\) are given as \(67^{\circ}\) each).

Step3: Solve the equation for \(x\)

$$
LATEXBLOCK0
$$

Answer:

\(46\)