Question

type the correct answer in each box. use numerals instead of words. if necessary, use / for the fraction bar(s).
abcd is a rectangle. the length of \\(\overline{bd}\\) is 8 units, and \\(m\angle abd\\) is \\(67^\circ\\).
the length of \\(\overline{ac}\\) is \\(___\\) units, and \\(m\angle cbd\\) is \\(___\\) \\(^\circ\\).

Explanation:

Step1: Find length of $\overline{AC}$

In a rectangle, diagonals are equal. $\overline{AC} = \overline{BD} = 8$ units.

Step2: Find $m\angle CBD$

Rectangle has right angles at vertices. $\angle ABC = 90^\circ$, so $m\angle CBD = 90^\circ - m\angle ABD$.
$m\angle CBD = 90^\circ - 67^\circ = 23^\circ$

Answer:

The length of $\overline{AC}$ is 8 units, and $m\angle CBD$ is 23°.