Chapter 11.8, Problem 31CCR

To determine

To find: What is the measure of the third angle in the triangle.

Answer to Problem 31CCR

Measure of third angle is ${65}^0$

Explanation of Solution

We know

External angle $=$ Sum of two opposite internal angles.

Using this concept for the given figure

We get

  $x^0+{\left(2x+1\right)}^0={115}^0$

  $\begin{array}{l}\Rightarrow x^0+2x^0+1^0={115}^0\\ \Rightarrow x^0+2x^0={115}^0-1^0\\ \Rightarrow x^0+2x^0={114}^0\\ \Rightarrow 3x^0={114}^0\\ \Rightarrow \frac{3x^0}{3}=\frac{{114}^0}{3}\\ \Rightarrow x^0=\frac{{114}^0}{3}\\ \Rightarrow x^0={38}^0\end{array}$

We know

Let $k$ be the third angle.

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

  $\begin{array}{l}\Rightarrow x^0+{\left(2x+1\right)}^0+k={180}^0\\ \Rightarrow {38}^0+{\left(2\left({38}^0\right)+1\right)}^0+k={180}^0\\ \Rightarrow {38}^0+{76}^0+1^0+k={180}^0\\ \Rightarrow {115}^0+k={180}^0\\ \Rightarrow k={180}^0-{115}^0\\ \Rightarrow k={65}^0\end{array}$

Therefore,

Measure of third angle is ${65}^0$