Question

dorothy and zeyad are practicing for a geometry test. dorothy randomly picks an angle listed on the figure below, and zeyad calculates its measurement. which of these are possible correct angle measures? select all that apply.

m∠cba = 28°
m∠dba = 62°
m∠fba = 90°
m∠dbc = 118°
m∠abc = 118°
m∠fbd = 180°

Explanation:

Step1: Identify right - angle

Since $\angle FBA = 90^{\circ}$ (marked as a right - angle in the figure), $m\angle FBA=90^{\circ}$ is correct.

Step2: Calculate $\angle CBA$

We know that $\angle FBC = 62^{\circ}$ and $\angle FBA = 90^{\circ}$. Then $m\angle CBA=m\angle FBA - m\angle FBC=90^{\circ}-62^{\circ}=28^{\circ}$.

Step3: Calculate $\angle DBC$

$\angle DBA = 90^{\circ}$ and $\angle CBA = 28^{\circ}$, so $m\angle DBC=m\angle DBA + m\angle CBA=90^{\circ}+28^{\circ}=118^{\circ}$. Also, $\angle ABC$ is the same as $\angle CBA$, so $m\angle ABC = 28^{\circ}$, not $118^{\circ}$. $\angle FBD$ is a straight - angle, so $m\angle FBD = 180^{\circ}$. And $m\angle DBA=90^{\circ}
eq62^{\circ}$.

Answer:

$m\angle CBA = 28^{\circ}$, $m\angle FBA = 90^{\circ}$, $m\angle DBC = 118^{\circ}$, $m\angle FBD = 180^{\circ}$