Question

In the figure, m_1=(2x) and m2 =(+69) (a) Write an equation to find r. Equation: 1 2. (b) Find the degree measure of ea m_1= 142=10

Answer 1

We have that angles 1 and 2 are supplemetary angles, therefore the sum of both of them must equal to 180, so:

$\begin{gathered} \measuredangle1+\measuredangle2=180 \\ \Rightarrow2x+(x+69)=180 \\ \Rightarrow2x+x+69=180 \\ \Rightarrow3x=180-69 \\ \Rightarrow3x=111\Rightarrow x=\frac{111}{3}=37 \\ x=37 \end{gathered}$

Now that we found the value for x, we simply substitute in the original values of angles 1 and 2 to find their measures:

$\begin{gathered} \text{For }\measuredangle1\colon \\ \measuredangle1=2x=2(37)=74 \\ \measuredangle1=74 \\ \text{For }\measuredangle2\colon \\ \measuredangle2=x+69=37+69=106 \\ \measuredangle2=106 \end{gathered}$

Therefore, angle 1 is 74 degrees and angle 2 is 106 degrees