Chapter 11.5, Problem 32STP

(a)

To determine

To find: The equation that represents the relationship between two angles.

Answer to Problem 32STP

The required equation is $2x+1+5x-9=90°$ .

Explanation of Solution

Given:

The measure of the two complementary angle is $2x+1$ and $5x-9$ .

Calculation:

Consider that the complementary angle is the angle that have measure of $90°$ .

Then,

  $2x+1+5x-9=90°$

(b)

To determine

To find: The degree of measure of each of the angle.

Answer to Problem 32STP

The measure of the two angles is $61$ and $29$ .

Explanation of Solution

Given:

The measure of the two complementary angle is $2x+1$ and $5x-9$ .

Calculation:

Consider the required equation is,

  $2x+1+5x-9=90°$

Then, solve further as,

  $\begin{array}{l}2x+1+5x-9=90°\\ 6x-8=90°\\ 7x=98\\ x=14\end{array}$

Then, the measure of the first angle is,

  $\begin{array}{l}2x+1=14\\ x=29\end{array}$

The second angle is.

  $\begin{array}{l}5x-9=5\left(14\right)-9\\ x=61\end{array}$

Thus, the measure of the two angles is $61$ and $29$ .