Chapter 11.1, Problem 31IP

a.

To determine

To find: The value of $x$ .

Answer to Problem 31IP

Value of $x$ is ${30}^0$

Explanation of Solution

Given information:

Pair of angles

From the given figure we can say that

Both angles forms a right angle it means they are complementary angles.

It means sum of their measure is ${90}^0$

  $x^0+2x^0={180}^0$ is the equation to find the value of $x$

We get

  $\begin{array}{l}\Rightarrow x^0+2x^0={90}^0\\ \Rightarrow 3x^0={90}^0\\ \Rightarrow x^0=\frac{{90}^0}{3}\\ \Rightarrow x^0={30}^0\end{array}$

Therefore,

Value of $x$ is ${30}^0$

b.

To determine

To find: Measure of two angles.

Answer to Problem 31IP

Two angles are ${60}^0$ and ${30}^0$

Explanation of Solution

Given information:

Pair of angles

From the given figure we can say that

Both angles forms a right angle it means they are complementary angles.

It means sum of their measure is ${90}^0$

  $x^0+2x^0={180}^0$ is the equation to find the value of $x$

We get

  $\begin{array}{l}\Rightarrow x^0+2x^0={90}^0\\ \Rightarrow 3x^0={90}^0\\ \Rightarrow x^0=\frac{{90}^0}{3}\\ \Rightarrow x^0={30}^0\end{array}$

One of the angles is $x={30}^0$

Other angle is $2x=2\left({30}^0\right)={60}^0$

Therefore,

Two angles are ${60}^0$ and ${30}^0$