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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There should be a typo in the question: the correct formula would be
Let's compute first. We have
If we intersect this set with X, we have
So, that would be the left hand side. For the right hand side, we have
And their union is again