Question

sept 5 1 #4 summative
if m∠def = 122, then what are m∠feg and m∠heg? the diagram is not to scale.
a. m∠feg = 122, m∠heg = 58
b. m∠feg = 58, m∠heg = 132
c. m∠feg = 68, m∠heg = 122
d. m∠feg = 58, m∠heg = 122

Explanation:

Step1: Recall linear - pair property

$\angle DEF$ and $\angle FEG$ form a linear - pair. The sum of angles in a linear - pair is $180^{\circ}$.

Step2: Calculate $m\angle FEG$

Let $m\angle FEG=x$. Since $m\angle DEF + x=180^{\circ}$ and $m\angle DEF = 122^{\circ}$, then $x=180 - 122=58^{\circ}$.

Step3: Recall vertical - angles property

$\angle DEF$ and $\angle HEG$ are vertical angles. Vertical angles are congruent. So $m\angle HEG=m\angle DEF = 122^{\circ}$.

Answer:

D. $m\angle FEG = 58,m\angle HEG = 122$