Question

17 look at the diagram below. given m∠1 = 30° use your knowledge of vertical and supplementary angles to find the measures of the other missing angles. m∠2 = m∠3 = m∠4 =

Explanation:

Step1: Identify vertical angles

Vertical angles are equal. $\angle1$ and $\angle3$ are vertical angles, and $\angle2$ and $\angle4$ are vertical angles.

Step2: Find measure of $\angle3$

Since $\angle1$ and $\angle3$ are vertical - angles and $m\angle1 = 30^{\circ}$, then $m\angle3=m\angle1 = 30^{\circ}$.

Step3: Find measure of $\angle2$

$\angle1$ and $\angle2$ are supplementary angles (they form a linear - pair), so $m\angle1 + m\angle2=180^{\circ}$. Substitute $m\angle1 = 30^{\circ}$ into the equation: $m\angle2=180^{\circ}-m\angle1=180 - 30=150^{\circ}$.

Step4: Find measure of $\angle4$

Since $\angle2$ and $\angle4$ are vertical angles, $m\angle4=m\angle2 = 150^{\circ}$.

Answer:

$m\angle2 = 150^{\circ}$
$m\angle3 = 30^{\circ}$
$m\angle4 = 150^{\circ}$