Chapter 11.1, Problem 30IP

To determine

To find: The measure of each angle.

Answer to Problem 30IP

  $\begin{array}{l}U={63}^0\\ V={113}^0\end{array}$

Explanation of Solution

Given information:

The ratio of measures is $7:13$

Angles $U$ and $V$ are supplementary angles.

Given

The ratio of measures is $7:13$

It means

  $U:V=7:13$

  $\begin{array}{l}\Rightarrow \frac{U}{V}=\frac{7}{13}\\ \Rightarrow U=\frac{7V}{13}\end{array}$

Given

Angles $U$ and $V$ are supplementary angles.

It means sum of their measure is ${180}^0$

  $U+V={180}^0$

On substituting values

We get

  $\begin{array}{l}U+V={180}^0\\ \Rightarrow \frac{7V}{13}+V={180}^0\\ \Rightarrow \frac{7V+13V}{13}={180}^0\\ \Rightarrow \frac{20V}{13}={180}^0\\ \Rightarrow V={180}^0\times \frac{13}{20}\\ \Rightarrow V=9\times 13\\ \Rightarrow V={117}^0\end{array}$

As we know

  $U=\frac{7V}{13}$

  $\begin{array}{l}\Rightarrow U=\frac{7\left(117\right)}{13}\\ \Rightarrow U=7\times 9\\ \Rightarrow U={63}^0\end{array}$

Therefore,

  $\begin{array}{l}U={63}^0\\ V={113}^0\end{array}$