Chapter 12, Problem 11CT

(a)

To determine

To classify: The triangle shown by its sides.

Answer to Problem 11CT

By the definition of triangles the given triangle is an isosceles triangle.

Explanation of Solution

Given:

The given figure is as follows.

  

Calculation:

Consider the measure of the base of the triangle is 100 Roman feet.

The measures of the other two sides of the triangle are both 144 Roman feet.

The objective is to classify the triangle shown by its sides.

From the given data, two sides of the triangle are congruent.

Therefore, by the definition of triangles the given triangle is an isosceles triangle.

(b)

To determine

To find: The measure of $\angle 1$ and $\angle 2$ .

Answer to Problem 11CT

The measures of $\angle 1$ and $\angle 2$ are $70°$ .

Explanation of Solution

Given:

The measure of $\angle 3$ is $40°$ .

Calculation:

Since two sides of the triangle are congruent, so by Base Angles Theorem $\angle 1\cong \angle 2$ .

So, let $m\angle 1=m\angle 2=x°$ , then by Triangle Sum Theorem,

  $\begin{array}{c}m\angle 1+m\angle 2+m\angle 3=180\\ x+x+40=180\\ 2x=140\\ x=70°\end{array}$

Therefore, the measures of $\angle 1$ and $\angle 2$ are $70°$ .