Question

1. in the figure, m∠1 = m∠2 = 22 and m∠3 = m∠4 = 123. find m∠tsk. 35 22 33 45

Explanation:

Step1: Recall linear - pair property

A linear - pair of angles is supplementary. Since $\angle3$ and $\angle SKT$ form a linear pair, and $m\angle3 = 123^{\circ}$, then $m\angle SKT=180 - 123=57^{\circ}$.

Step2: Use angle - sum property of a triangle

In $\triangle STK$, we want to find $m\angle TSK$. We know that $m\angle1 = 22^{\circ}$ and $m\angle SKT = 57^{\circ}$.
By the angle - sum property of a triangle ($m\angle1+m\angle TSK+m\angle SKT = 180^{\circ}$ in $\triangle STK$), we can solve for $m\angle TSK$.
Let $x=m\angle TSK$. Then $x+22 + 57=180$.
$x=180-(22 + 57)$.
$x = 180 - 79$.
$x = 33^{\circ}$.

Answer:

$33$