Question

ZA and ZB are supplementary angles. If m A = (3x – 17)° and mZB = (2x – 23)º, then find the measure of ZB.

Answer 1

Since angle A and angle B are supplementary, then their sum equals 180, and we have the following equation:

$\measuredangle A+\measuredangle B=180$

in this case, we have the following:

$(3x-17)+(2x-23)=180$

solving for 'x', we get:

$\begin{gathered} 3x-17+2x-23=180 \\ \Rightarrow5x-40=180 \\ \Rightarrow5x=180+40=220 \\ \Rightarrow x=\frac{220}{5}=44 \\ x=44 \end{gathered}$

now that we have that x = 44, we can find the measure of angle B:

$\begin{gathered} \measuredangle B=2(44)-23=88-23=65 \\ \Rightarrow\measuredangle B=65\degree \end{gathered}$

therefore, the measure of angle B is 65 degrees