Question

Two angles are complementary. The measurement of ∠GHI ∠GHI  is (5x+6)∘(5x+6)∘ and ∠JKL ∠JKL  measures (3x+4)∘(3x+4)∘. What are the measures of the two angles?

Answer 1

The angles ∠GHI and ∠JKL are complementary, this means that they add up to 90°

Then we can say that

`\angle\text{GHI}+\angle\text{JKL}=90^(\circ)`

For

∠GHI= (5x+6)°

∠JKL= (3x+4)°

`(5x+6)+(3x+4)=90`

From this expression you can calculate the value of x

First step is to order the like terms together and simplify them}

`\begin{gathered} 5x+3x+6+4=90 \\ 8x+10=90 \\ 8x=90-10 \\ 8x=80 \end{gathered}`

Next divide both sides of the equation by 8 to reach the value of x

`\begin{gathered} (8x)/(8)=(80)/(8) \\ x=10 \end{gathered}`

Now that we knoe the value of x, we can calculate the measure of both angles

`\begin{gathered} \angle\text{GHI}=5x+6 \\ \angle\text{GHI}=5\cdot10+6 \\ \angle\text{GHI}=56 \end{gathered}`
`\begin{gathered} \angle\text{JKL}=3x+4 \\ \angle\text{JKL}=3\cdot10+4 \\ \angle\text{JKL}=34 \end{gathered}`