Question

10. Find the measure of each missing angle.mZ1 =m2 =1272.mz3 =59m24 =5/43m25 =

Answer 1

From the figure shown we notice that the angles 127° and 2 are supplementary, that means that:

$\begin{gathered} 127+m\angle2=180 \\ m\angle2=180-127 \\ m\angle2=53 \end{gathered}$

We also notice that

$m\angle2+m\angle3+m\angle4=180$

and

$m\angle1+59+127+m\angle5=360$

furthermore

$m\angle5+m\angle4=180$

And

$m\angle1+m\angle3+59=180$

so we have the system of equations:

$\begin{gathered} m\angle3+m\angle4=127 \\ m\angle1+m\angle5=174 \\ m\angle5+m\angle4=180 \\ m\angle1+m\angle3=121 \end{gathered}$

Solving for the angle 1 in the fourth equation we have

$m\angle1=121-m\angle3$

plugging this value in the second equation we have

$\begin{gathered} 121-m\angle3+m\angle5=174 \\ -m\angle3+m\angle5=53 \\ m\angle5=m\angle3+53 \end{gathered}$

Plugging this value in the third equation we have