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. Angle $d$ and the $122^{\circ}$ angle are vertical angles, so $d = 122^{\circ}$.

Step2: Use angle - addition property

The sum of angles around a point is $360^{\circ}$. Let's consider the angles around the intersection point. We know one angle is $122^{\circ}$ (equal to $d$), another is $24^{\circ}$, and we want to find $e$ and $f$. Also, since $d = 122^{\circ}$, and the non - overlapping angles near the $122^{\circ}$ angle and $24^{\circ}$ angle are $e$ and $f$. We know that $e + f+24^{\circ}=180^{\circ}$ (a straight - line angle is $180^{\circ}$).

Step3: Calculate angle $e$

Since $d = 122^{\circ}$, and the angle adjacent to $d$ and the $24^{\circ}$ angle form a straight line. So $e=180^{\circ}-122^{\circ}-24^{\circ}=34^{\circ}$.

Step4: Calculate angle $f$

Since $e + f=180^{\circ}-24^{\circ}=156^{\circ}$ and $e = 34^{\circ}$, then $f=156^{\circ}-e$. So $f = 34^{\circ}$.

Answer:

$d = 122^{\circ}$, $e = 34^{\circ}$, $f = 34^{\circ}$