Question

problem 1 determine the measure of each angle. angle measure (degrees) adb 53 bdc cde fde fda

Explanation:

Step1: Identify complementary angle

Since $\angle ADB = 53^{\circ}$ and $\angle BDC$ is complementary to $\angle ADB$ (as $\angle ADC = 90^{\circ}$), we use the formula $\angle BDC=90^{\circ}-\angle ADB$.
$\angle BDC = 90 - 53=37^{\circ}$

Step2: Identify vertical - angle

$\angle CDE$ and $\angle ADB$ are vertical - angles. Vertical angles are equal. So $\angle CDE=\angle ADB = 53^{\circ}$

Step3: Identify complementary angle

$\angle FDE$ and $\angle CDE$ are complementary (as $\angle FDC = 90^{\circ}$). So $\angle FDE=90^{\circ}-\angle CDE$.
$\angle FDE = 90 - 53 = 37^{\circ}$

Step4: Identify straight - angle

$\angle FDA$ is a straight - angle, so $\angle FDA = 180^{\circ}$

Answer:

Angle	Measure (degrees)
$BDC$	$37$
$CDE$	$53$
$FDE$	$37$
$FDA$	$180$