Question

I need help with this question. it is difficult for me and i tried working on it

Answer 1

`\angle3=33º`

Step-by-step explanation:

If two angles are supplentary, their sum is equal to 180º

If two angles are complementary, their sum is equal to 90º

We know:

`\begin{gathered} \angle1=(8x+3)º \\ \angle2=(5x-18)º \end{gathered}`

Also,

`\begin{gathered} \angle1+\angle2=180º \\ \angle2+\angle3=90º \end{gathered}`

Now, we can write:

And solve for x:

`\begin{gathered} 8x+3+5x-18=180 \\ 13x-15=180 \\ 13x=180+15 \\ . \\ x=(195)/(13) \\ . \\ x=15 \end{gathered}`

Now we can find the measure of angle 2:

`\angle2=(5x-18)º\Rightarrow\angle2=(5\cdot15-18)º=(75-18)º=57º`

And since angle 2 and 3 are complementary:

`\angle2+\angle3=90º\Rightarrow57º+\angle3=90º`

And solve:

`\begin{gathered} 57º+\angle3=90º \\ \angle3=90º-57º \\ \angle3=33º \end{gathered}`