Chapter 11.1, Problem 3BGP

To determine

To calculate: The measure of $\angle UVW$ .

Answer to Problem 3BGP

The measure of $\angle UVW={54}^0$ .

Explanation of Solution

Given information: Given, $\angle RVT$ and $\angle UVW$ are vertical angles. Also given, $m\angle RVT=3x^0$ and $m\angle UVW={(5x-36)}^0$ .

Calculation:

  $\angle RVT$ and $\angle UVW$ are vertical angles.

We know that, vertical angles are equal.

  $\therefore$ We can write,

  $\begin{array}{l}\angle RVT=\angle UVW\\ \Rightarrow 3x=5x-36\\ \Rightarrow 5x-36=3x\\ \Rightarrow 5x-36-3x=0\\ \Rightarrow 5x-3x=36\\ \Rightarrow 2x=36\\ \Rightarrow x=\frac{36}{2}\\ \Rightarrow x=18\end{array}$

  $\therefore$ The value of $x=18$ .

  $\therefore$ We will get,

  $\begin{array}{}$ m\angle UVW={(5x-36)}^0$$ ={(5\times 18-36)}^0$$ ={(90-36)}^0$$ ={54}^0$\end{array}$

  $\therefore$ The measure of $\angle UVW={54}^0$