Q 4.36 - Intermediate Algebra

Question

Translate to a system of equations and then solve:

Two angles are supplementary. The measure of the larger angle is $18$ less than twice the measure of the smaller angle. Find the measures of the angles.

Step-by-Step Solution

Answer

The measure of the angles are ${66}^{\circ }$ and ${114}^{\circ }$.

Step 1 . Given

We are given two supplementary angles and larger angle is $18$ less than twice the measure of the smaller angle.

Step 2. Assumptions and formation of equations.

Let the smaller angle be $x$ and larger angle be $y$

We know that the sum of supplementary angles is equal to ${180}^{\circ }$. so

 $x+y={180}^{\circ }$

Also, the other equation will be $y=2x-18$.

Step 3 . Solving the equations

Putting the value of $y$ in first equation, we get

$$\begin{gathered} x+2x-18={180}^{\circ } \\ 3x-18={180}^{\circ } \end{gathered}$$

Adding $18$ both sides, we get

$3x={198}^{\circ }$

Dividing by $3$,

$x={66}^{\circ }$

Putting the value of $x$ in second equation, we get

$$\begin{gathered} y=2\times 66-18 \\ ={114}^{\circ } \end{gathered}$$

Step 4. Checking the solution

Checking the solution by putting the value of $x,y$ in the equations, we get

$$\begin{gathered} x+y={180}^{\circ } \\ {66}^{\circ }+{114}^{\circ }={180}^{\circ } \\ {180}^{\circ }={180}^{\circ } \\ y=2x-14 \\ {114}^{\circ }=2\left({66}^{\circ }\right)-18 \\ {114}^{\circ }={132}^{\circ }-18 \\ {114}^{\circ }={114}^{\circ } \end{gathered}$$

This is true, hence the solution is correct.