Question

find $m\angle tqw$.
$m\angle tqw = \square^\circ$
(there is a diagram with lines intersecting at point q, angles of 67° between rq and zq, and between xq and yq, and points t, w on other lines from q)

Explanation:

Step1: Identify straight angle sum

A straight angle equals $180^\circ$. For line $RX$, $\angle ZQR + \angle ZQY + \angle YQX = 180^\circ$.

Step2: Calculate $\angle ZQY$

Substitute known values:
$\angle ZQY = 180^\circ - 67^\circ - 67^\circ = 46^\circ$

Step3: Use vertical angles property

$\angle TQW$ and $\angle ZQY$ are vertical angles, so they are congruent.
$m\angle TQW = m\angle ZQY$

Answer:

$46$