Question

find the measure of the missing angles. answer attempt 1 out of 2 d = 122° e = 24° f =

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. Since the angle opposite to the $122^{\circ}$ angle is $d$, then $d = 122^{\circ}$. Also, the angle opposite to the $24^{\circ}$ angle is $e$, so $e=24^{\circ}$.

Step2: Use angle - sum property

The sum of angles around a point is $360^{\circ}$. Let's find $f$. We know two of the angles are $122^{\circ}$ and $24^{\circ}$, and their vertical - angle counterparts are also part of the angles around the point. So, $f=360-(122 + 122+24 + 24)$.
$f=360 - 292$.
$f = 68^{\circ}$

Answer:

$f = 68^{\circ}$