ANSWER and EXPLANATION
We are given that m<8 = 23 degrees.
First, let us find m<7.
m<7 and m<8 are angles on a straight line. Angles lying on a straight line sum up to 180 degrees.
This means that:
23 + m<7 = 180
m<7 = 180 - 23
m<7 = 157 degrees
Since m<8 and m<5 also lie on a straight line, we have that:
m<5 = 157 degrees
m<8 and m<6 are vertically opposite angles. Vertically opposite angles are equal, therefore:
m<6 = 23 degrees
m<8 and m<4 are corresponding angles, based on their positions. Corresponding angles are equal, therefore:
m<4 = 23 degrees
m<4 and m<2 are vertically opposite angles, therefore:
m<2 = 23 degrees
m<5 and m<1 are corresponding angles, therefore:
m<1 = 157 degrees
m<1 and m<3 are vertically opposite angles, therefore:
m<3 = 157 degrees