Question

If a || b, m<2=63°, and m<9=105°, find the missing measure of m<13=?

Answer 1

Lines a and b are parallel, you know that m∠2=63º and m∠9=105º

m∠2 and m∠5 are vertically opposite angles, which means that they are congruent, so that:

`m\angle2=m\angle5=63º`

Now, looking at the angles formed when lines a and b are intersected by line c

The angle formed by the sum of m∠5 and m∠4 and the angle m∠9 are corresponding angles, which means that they are congruent, you can express this as follows:

`m\angle9=m\angle5+m\angle4`

Knowing the measures of m∠9 and m∠5 we can determine the measure of m∠4:

`\begin{gathered} 105=63+m\angle4 \\ m\angle4=105-63 \\ m\angle4=42º \end{gathered}`

Finally, you have to look at the angles formed when line d crosses the lines a and b:

m∠4 and m∠13 can be linked with an F-shaped line, which indicates that they are corresponding angles. This means that they are congruent so that:

`m\angle4=m\angle13=42º`