Question

2 angles are supplementary period, the first angle measures (10x+3),and the second measures (15x-5). write an equation to determine the value of x , then solve your equation and find the measures of both angles.

Answer 1

The first angle is

`(10x+3)`

The second angle is

`(15x-5)`

These two angles are supplementary.

This means that the sum of these two angles is equal to 180°

So, we can write the equation as

`(10x+3)+(15x-5)=180`

Now let us solve this equation for x.

`\begin{gathered} 10x+3+15x-5=180 \\ 10x+15x+3-5=180 \\ 25x-2=180 \\ 25x=180+2 \\ 25x=182 \\ x=(182)/(25) \\ x=7.28 \end{gathered}`

Now we can find both angles

`\begin{gathered} 10x+3=10(7.28)+3=72.8+3=75.8\degree \\ 15x-5=15(7.28)-5=109.2-5=104.2\degree_{}_{} \end{gathered}`

Therefore,

x = 7.28

first angle = 75.8°

second angle = 104.2°