Question

a beam of light and a mirror can be used to study the behavior of light. light that strikes the mirror is reflected so that the angle of reflection and the angle of incidence are congruent. in the diagram, ∠abc has a measure of 52°.
a. name the angle of reflection and find its measure.
b. find m∠abd.
c. find m∠abe and m∠dbf.
a. name the angle of reflection and find its measure.
the angle of reflection is ∠\boxed{} and has a measure of \boxed{}°.

Explanation:

Step1: Identify reflection angle

Given angle of incidence $\angle ABC = 52^\circ$, and angle of incidence $\cong$ angle of reflection, so $\angle DBC = 52^\circ$.

Step2: Calculate $\angle ABD$

$\angle ABD = \angle ABC + \angle DBC$
$\angle ABD = 52^\circ + 52^\circ = 104^\circ$

Step3: Calculate $\angle ABE$

$\angle ABE + \angle ABC = 90^\circ$ (right angle)
$\angle ABE = 90^\circ - 52^\circ = 38^\circ$

Step4: Calculate $\angle DBF$

$\angle DBF + \angle DBC = 90^\circ$ (right angle)
$\angle DBF = 90^\circ - 52^\circ = 38^\circ$

Answer:

a. The angle of reflection is $\angle DBC$ and has a measure of $52^\circ$.
b. $m\angle ABD = 104^\circ$
c. $m\angle ABE = 38^\circ$, $m\angle DBF = 38^\circ$