Answer:
From the picture attached,
There are two parallel lines intersected by three transverse lines.
m∠2 = 98°, m∠3 = 23°, m∠8 = 70°
a). Since ∠1 and ∠2 are linear pairs,
=
m∠1 + m∠2 = 180°
m∠1 + 98° = 180°
m∠1 = 180 - 98
m∠1 = 82°
b). m∠4 = m∠7 [Corresponding angles]
m∠7 = 180° - (m∠2 + m∠3) [Property of a triangle]
= 180 - (98 + 23)
= 180 - 121
= 59°
m∠4 = m∠7 = 59°
c). m∠5 = 180° - (m∠3 + m∠4)
= 180° - (23° + 59°)
= 180° - 82°
= 98°
d). m∠6 = 180° - (m∠7 + m∠8)
= 180° - (59° + 70°)
= 180 - 129
= 51°
e). m∠7 = 59° [Calculated in part b]
f). m∠9 = 180° - (m∠4 + m∠8) [Property of a triangle]
= 180° - (59 + 70)°
= 180 - 129
= 51°
g). m∠10 = 180° - m∠9
= 180 - 51
= 129°