Question

find the measure of the missing angles. answer attempt 2 out of 2 d = 102° e = ° f = 36°

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. Since $d$ and the $102^{\circ}$ angle are vertical angles, $d = 102^{\circ}$. Since $f$ and the $36^{\circ}$ angle are vertical angles, $f=36^{\circ}$.

Step2: Use angle - sum property around a point

The sum of angles around a point is $360^{\circ}$. Let's find $e$. We know that $36^{\circ}+102^{\circ}+d + e+f=360^{\circ}$. Substitute $d = 102^{\circ}$ and $f = 36^{\circ}$ into the equation: $36^{\circ}+102^{\circ}+102^{\circ}+e + 36^{\circ}=360^{\circ}$. Combine like - terms: $(36^{\circ}+102^{\circ}+102^{\circ}+36^{\circ})+e=360^{\circ}$, $276^{\circ}+e = 360^{\circ}$. Then $e=360^{\circ}-276^{\circ}=84^{\circ}$.

Answer:

$e = 84$