Question

angle measures complete the statement given that s ⊥ t. 32. if m∠3 = 42°, then m∠1 = ＿？＿.

Explanation:

Step1: Note vertical - angle relationship

Vertical angles are equal. $\angle3$ and $\angle6$ are vertical angles, so $m\angle6 = m\angle3$. Since $m\angle3=42^{\circ}$, then $m\angle6 = 42^{\circ}$.

Step2: Use right - angle property

Given $s\perp t$, $\angle5$ is a right - angle and $m\angle5 = 90^{\circ}$. Also, $\angle5+\angle6+\angle1=180^{\circ}$ (because they form a straight line).

Step3: Solve for $m\angle1$

Substitute the known values into the equation $m\angle5+\angle6+\angle1 = 180^{\circ}$. We know $m\angle5 = 90^{\circ}$ and $m\angle6 = 42^{\circ}$. So, $90^{\circ}+42^{\circ}+m\angle1=180^{\circ}$. Then $m\angle1=180^{\circ}-(90^{\circ} + 42^{\circ})=48^{\circ}$.

Answer:

$48^{\circ}$