Chapter 11, Problem 6CR

To determine

To find: The Value of $x$ .

Answer to Problem 6CR

Value of $x$ is ${45}^0$ and the triangle is Acute scalene

Explanation of Solution

Given information:

Two angles of a triangle are ${51}^0$ and ${84}^0$

  $x$ is the third angle.

We know

Sum of angles of a triangle is ${180}^0$

Using that

We get

  $\begin{array}{l}x+{51}^0+{84}^0={180}^0\\ \Rightarrow x+{135}^0={180}^0\\ \Rightarrow x+{135}^0-{135}^0={180}^0-{135}^0\\ \Rightarrow x={180}^0-{135}^0\\ \Rightarrow x={45}^0\end{array}$

The triangle has no Obtuse angle

Th triangle has no congruent sides

So, the triangle is Acute scalene.

Therefore,

Value of $x$ is ${45}^0$ and the triangle is Acute scalene