Question

find the angle measurements of the following below and justify why by describing angle relationships.

Answer 1

The first step is to find the value of x. The sum of angles (2x+10) and (3x-5) is 180 because they are consecutive interior angles

`\begin{gathered} (2x+10)+(3x-5)=180 \\ 2x+3x+10-5=180 \\ 5x+5=180 \\ 5x=180-5 \\ 5x=175 \\ x=(175)/(5) \\ x=35 \end{gathered}`

Now, you can find the measure of 3 of the angles

`\begin{gathered} 2x+10=2\cdot35+10=70+10=80 \\ 2x-20=2\cdot35-20=70-20=50 \\ 3x-5=3\cdot35-5=105-5=100 \end{gathered}`

The sum of 2x-20 and angle 1 is 180 because they are consecutive interior angles, use this to find angle 1 measurement

`\begin{gathered} 50+\measuredangle1=180 \\ \measuredangle1=180-50 \\ \measuredangle1=130 \end{gathered}`