Question

line q and line M are cut by transversal lines J&K the lines and the measures of some of the angles created by the intersections of the lines are shown in the diagram below. What is the measure of angle 5?​

Answer 1

The angle of 110° and the angle labelled as 1 form 180°, so we have

$<1> = 180-110=70$

The same holds for the angle labelled 2 and the 115° angle:

$<2> = 180-115=65$

Angle 1, 2 and 7 are the interior angles of a triangle, so they sum to 180. We can deduce

$<7> = 180-70-65=45$

Angles 5 and 7 are corresponding angles, so they have the same measure.