Question

If p || , m<7 = 131°, and m<16 = 88°, find the measure of the missing angle m<4= ?

Answer 1

According to the theorem, the corresponding angles, formed by a transversal on a pair of parallel sides, are always equal.

Also, the sum of angles on a straight line is 180 degree.

The angles 5 and 7 constitute a pair of corresponding angles, formed by the transversal 'r' on the pair of parallel sides 'p' and 'q'. So they must be equal,

`\begin{gathered} \angle5=\angle7 \\ \angle5=131^(\circ) \end{gathered}`

The angles 4 and 5 constitute a straight line, so they must add up to be 180 degrees,

`\begin{gathered} \angle4+\angle5=180^(\circ) \\ \angle4+131^(\circ)=180^(\circ) \\ \angle4=180^(\circ)-131^(\circ) \\ \angle4=49^(\circ) \end{gathered}`

Thus, the angle 4 measures 49 degrees.