Question

If p || , m<7 = 131°, and m<16 = 88°, find the measure of the missing angle m<3=?

Answer 1

According to the property, the alternate interior angles, formed by a transversal on two parallel sides, are always equal.

Consider that in the given diagram, the lines 'p' and 'q' are parallel, and line 'r' acts as the transversal on the lines 'p' and 'q'.

And the angles 3 and 7 constitute a pair of alternate interior angles, formed by the transversal 'r' on the parallel sides 'p' and 'q'. So they must be equal,

`\begin{gathered} \angle7=\angle3 \\ \angle3=131^(\circ) \end{gathered}`

Thus, the angle 3 measures 131 degrees.