Question

3. If ZCAB measures108°, what is themeasure of ZCAD ?CADB

Answer 1

GIVEN:

We are given a parallelogram labeled ABCD with angle CAB meauring 108 degrees as indicated.

Required:

Find the measure of angle CAD

Step by step solution;

First, we need to take note of some of the properties of a parallelogram.

"Opposite angles are equal."

"Diagonals bisect each other."

"Diagonals form two congruent triangles."

With these in mind, we observe that the diagonal AD bisects diagonla CB into two halves.

Take note also of the angle bisector theorem, which states;

"If a ray bisects an angle of a triangle, then it divides the opposite side of the triangle into segments that are proportional to the other two sides."

In other words, the diagonal AD bisects the line CB into side lengths proportional to the divided angle CAB. Line CB has been divided into two halves, which simply means that the diagonal AD has effectively divided angle CAB into two halves namely;

`\angle CAD\text{ }and\text{ }\angle BAD`

Therefore;

`\begin{gathered} \angle CAD=\angle BAD=(\angle CAB)/(2) \\ \\ \angle CAD=\angle BAD=(108)/(2) \\ \\ \angle CAD=\angle BAD=54\degree \end{gathered}`

ANSWER:

`\angle CAD=54\degree`