Question

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 °.

Answer 1

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

Answer 2

AC = 8 units

Angle CDB = 67°

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°