Angle of 59° is congruent to angle 6, then:
m<6 = 59°
the sum of the interior angles of a triangle is equal to 180°, then, you have:
m<9 + m<6 + 59 = 180
replace the value of m<6 and calculate m<9:
m<9 + 59 + 59 = 180
m<9 + 118 = 180
m<9 = 180 - 118
m<9 = 62°
angle 9 is congruent to angle 8:
m<8 = 62°
angle 8 and angle 10 are supplementary, then:
m<8 + m<10 = 180
62 + m<10 = 180
m<10 = 180 - 62
m<10 = 118°
angle 10 is congruent to angle 7:
m<7 = 118°
angles 5 and 6 are complementary, then:
m<5 + m<6 = 90
m<5 + 59 = 90
m<5 = 90 - 59
m<5 = 31°
angle 4 and 5 are congruent:
m<4 = 31°
angles 3 and 4 are complementaries:
m<3 + m<4 = 90
m<3 + 31 = 90
m<3 = 90 - 31
m<3 = 59°
m<1 = 59°
m<2 = m<11 = 31°
