Question

problem 6 this diagram includes supplementary, complementary, and vertical angles. determine each of the missing angle measures. angle measure (degrees) abc cbd dbe fba

Explanation:

Step1: Identify vertical - angle relationship

Since $\angle FBA$ and the $56^{\circ}$ angle are vertical angles, they are equal. So $\angle FBA = 56^{\circ}$.

Step2: Identify complementary - angle relationship

$\angle FBE = 90^{\circ}$, and $\angle FBA+\angle ABE = 90^{\circ}$. Since $\angle FBA = 56^{\circ}$, then $\angle ABE=90 - 56=34^{\circ}$. Also, $\angle DBE = 90^{\circ}$ (given right - angle).

Step3: Identify supplementary - angle relationship

$\angle ABC$ and $\angle CBD$ are supplementary (a straight - line is $180^{\circ}$). $\angle ABC$ and $\angle DBE$ are vertical angles, so $\angle ABC = 90^{\circ}$. Then $\angle CBD=180 - 90 = 90^{\circ}$.

Answer:

Angle	Measure (degrees)
$CBD$	$90$
$DBE$	$90$
$FBA$	$56$