Question

adjacent angles <1 and <2 are complementary angles. the measure of <1 is 35°. the measure of <2 is (8x-1)°. Find a)the value of x. b)find the measure of <2. c)explain how the measures let you check your work

Answer 1

a) x=18.25

b)

`\text{angle }\measuredangle2=145`

Step-by-step explanation

Step 1

Two angles are called complementary when their measures add to 90 degrees.

it means

`\text{angle }\measuredangle1\text{ +angle}\measuredangle2=90`

replacing

`\begin{gathered} 35+(8x-1)=180 \\ 35+8x-1=180 \\ \text{add similater terms} \\ 8x+34=180\text{ Equation} \end{gathered}`

Step 2

solve the equation

`\begin{gathered} 8x+34=180 \\ \text{subtract 34 in both sides} \\ 8x+34-34=180-34 \\ 8x=146 \\ \text{divide both sides by 8} \\ (8x)/(8)=(146)/(8) \\ x=18.25 \end{gathered}`

so,x=18.25

Step 3

find the measure of 2

`\begin{gathered} \text{angle }\measuredangle2=8x-1 \\ \text{replacing} \\ \text{angle }\measuredangle2=8(18.25)-1 \\ \text{angle }\measuredangle2=146-1 \\ \text{angle }\measuredangle2=145 \end{gathered}`

I hope this helps you