Question

Find the measure of each numbered angle and name the theorem or postulate that justify your work.

Answer 1

m∠2 = 94

m∠3 = 94

Step-by-step explanation:

Angle 2 and 3 are vertical angles. They are opposite and are formed when two lines cross. Since they are vertical angles, they have the same measure, so we can write the following equation:

`\begin{gathered} m\angle2=m\angle3 \\ 4x-26=3x+4 \end{gathered}`

So, solving for x, we get:

`\begin{gathered} 4x-26+26=3x+4+26 \\ 4x=3x+30 \\ 4x-3x=3x+30-3x \\ x=30 \end{gathered}`

Now, we can calculate the measure of angle 2 and 3 as:

`\begin{gathered} m\angle2=4x-26=4\cdot30-26=120-26=94 \\ m\angle3=3x+4=3\cdot30+4=90+4=94 \end{gathered}`

Therefore, the measures of angles 2 and 3 are 94