Chapter 9.9, Problem 5P

To determine

To calculate:

Measure of three angles.

Answer to Problem 5P

Measure of three angles is $x=30°,y=80°,z=70°$ .

Explanation of Solution

Given information:

Measure of largest angle is $20°$ more than twice the measure of the smallest angle.

Five times the measure of the smallest angle equals the sum of measures of other two angles.

Calculation:

Let, $x$ represents the smallest angle, $y$ represents the largest angle and $z$ represents the third angle.

Equations will get,

  $\begin{array}{l}y-2x=20\\ y+z-5x=0\\ x+y+z=180\end{array}$

Make $y$ the subject of the formula,

  $y=20+2x$ and $y=5x-z$

Equate both of them,

  $20+2x=5x-z\to z=3x-20$

Substitute into final equation,

  $x+20+2x+3x-20=6x=180\to x=30$

Now, solve for $y$ ,

  $y=20+2\left(30\right)=80$

Now, solve for $z$ ,

  $z=180-80-30=70$

Thus, Measure of three angles is $x=30°,y=80°,z=70°$ .