Question

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

Explanation:

Step1: Identify vertical angles

Vertical - angles are equal. Angle $d$ and the $77^{\circ}$ angle are vertical angles, so $d = 77^{\circ}$. Angle $e$ and the $31^{\circ}$ angle are vertical angles, so $e = 31^{\circ}$.

Step2: Use angle - sum property

The sum of angles around a point is $360^{\circ}$. We know two angles are $77^{\circ}$ and $31^{\circ}$, and their vertical - angle counterparts are also $77^{\circ}$ and $31^{\circ}$. Let's find $f$.
\[f=360-(77 + 77+31 + 31)\]
\[f = 360 - 288\]
\[f = 72^{\circ}\]

Answer:

$d = 77^{\circ}$, $e = 31^{\circ}$, $f = 72^{\circ}$