Question

answer attempt 1 out of 2
$d = 102^{circ}$ $e = 36^{circ}$ $f=square^{circ}$

Explanation:

Step1: Recall vertical - angle property

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

Step2: Use the angle - sum property of a straight - line

The sum of angles on a straight - line is $180^{\circ}$. Consider the straight - line with angles $d$, $e$, and $f$. We know that $d + e+f=180^{\circ}$. Substitute $d = 102^{\circ}$ and $e = 36^{\circ}$ into the equation: $102^{\circ}+36^{\circ}+f = 180^{\circ}$.

Step3: Solve for $f$

First, simplify the left - hand side of the equation: $138^{\circ}+f=180^{\circ}$. Then, subtract $138^{\circ}$ from both sides: $f=180^{\circ}-138^{\circ}=42^{\circ}$.

Answer:

$42$