Question

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

Explanation:

Step1: Use vertical - angle property

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

Step2: Find the sum of angles around a point

The sum of angles around a point is $360^{\circ}$. Let's consider the angles at the intersection. We know one angle is $122^{\circ}$ and another is $24^{\circ}$. Also, $d = 122^{\circ}$. Let's find $e$. First, we know that the non - overlapping angles adjacent to $e$ and the given angles make up a full - circle of angles. We can also use the fact that linear pairs of angles (angles that form a straight line) sum to $180^{\circ}$. The angle adjacent to $e$ and the $24^{\circ}$ angle and part of the $122^{\circ}$ angle form a straight line. So, $e=180^{\circ}-(24^{\circ} + 82^{\circ})=74^{\circ}$.

Step3: Use vertical - angle property for $f$

The angle opposite to $f$ is $24^{\circ}$, so $f = 24^{\circ}$ by the vertical - angle property.

Answer:

$d = 122^{\circ}$, $e = 74^{\circ}$, $f = 24^{\circ}$