Chapter 6, Problem 37SGR

To determine

The measure of angle ACB.

Answer to Problem 37SGR

  $m\angle ACB=35$

Explanation of Solution

Given:

ABCD is a rhombus.

  $EB=9,AB=12\text{ and m}\angle ABD=55.$

Calculation:

According to the Theorem of Diagonals of a Rhombus;

As the given figure is a rhombus, its diagonals are perpendicular.

Therefore,

  $\angle AEB$ is a right angle and hence, triangle AEB is a right triangle.

Also, the acute angles of a right triangle are complementary to each other.

Consider the right triangle AEB;

  $\begin{array}{l}m\angle BAC+m\angle ABD=90\\ m\angle BAC+55=90\\ m\angle BAC=90-55\\ m\angle BAC=35\end{array}$

A rhombus has 4 congruent sides. So, triangle ABC is an isosceles triangle.

According to the Isosceles Triangle theorem;

  $\begin{array}{l}\angle ACB\cong \angle BAC\\ m\angle ACB=m\angle BAC\\ m\angle ACB=35\end{array}$