ABCD is a rectangle. The length of BD is 8 units, and m angle ABD is 67°. The length of AC is units, and m angle CDB is °.
2 answers:
Answer:
AC = 8 units
Angle CDB = 67°
Step-by-step explanation:
The given figure represents the data given.
From figure we can see that BD = AC
Length of AC = 8 units
We also have
∠ABD = ∠CDB
Angle CDB = 67°
See the attached picture to better understand the problem
we know that
in rectangle ABCD
AB=CD
and
AD=BC
therefore
the triangle ACD and triangle ABC are congruent
so
BD=AC
BD=8 units
the answer part a) is
BD= 8 units
Part b) Find angle CBD
we know that
∠ABD+∠CBD=90°---------> by complementary angles
so
∠CBD=90-∠ABD-----> 90-67----> 23°
∠CBD=23°
the answer Part b) is
∠CBD=23 degrees
we know that
in rectangle ABCD
AB=CD
and
AD=BC
therefore
the triangle ACD and triangle ABC are congruent
so
BD=AC
BD=8 units
the answer part a) is
BD= 8 units
Part b) Find angle CBD
we know that
∠ABD+∠CBD=90°---------> by complementary angles
so
∠CBD=90-∠ABD-----> 90-67----> 23°
∠CBD=23°
the answer Part b) is
∠CBD=23 degrees
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