Question

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

Explanation:

Step1: Recall angle - sum property

We know that $\angle3$ is an exterior angle of $\triangle STK$. By the exterior - angle property of a triangle, $\angle3=\angle1 + \angle TSK$.

Step2: Rearrange the formula to solve for $\angle TSK$

We can rewrite the formula as $\angle TSK=\angle3-\angle1$.

Step3: Substitute the given angle measures

Given that $\angle1 = 22^{\circ}$ and $\angle3 = 123^{\circ}$, then $\angle TSK=123 - 22$.
$\angle TSK = 35^{\circ}$

Answer:

$35$