Question

In the figure line m and line n are parallel. if m<3 =64 degrees:m<1 =m<4 =m<8 =m<10 = find each angle measurement

Answer 1

Angles 3 and 6 are Vertical Angles.

$\begin{gathered} m\angle6=m\angle3 \\ m\angle6=64\degree \end{gathered}$

Angles 1, 6, and 5 are on a straight line.

$\begin{gathered} m\angle1+m\angle5+m\angle6=180\degree \\ m\angle1+90\degree+64\degree=180\degree \\ m\angle1+154\degree=180\degree \\ m\angle1=180\degree-154\degree \\ m\angle1=26\degree \end{gathered}$$\begin{gathered} m\angle2=m\angle5(\text{Vertical Angles)} \\ \implies m\angle2=90\degree \\ m\angle4=m\angle1(\text{Vertical Angles)} \\ \implies m\angle4=26\degree \end{gathered}$

Since lines m and n are parallel, angles 3 and 10 are Alternate Angles.

$\begin{gathered} m\angle10=m\angle3(\text{Alternate Angles)} \\ m\angle10=64\degree \end{gathered}$

Angles 8 and 10 are Vertical Angles.

$\begin{gathered} m\angle8=m\angle10 \\ m\angle8=64\degree \end{gathered}$