Picture of question is in the attachment below :
Answer:
m∠1= 157°
m∠2= 23°
m∠3= 157°
m∠4= 23°
m∠5= 157°
m∠6= 23°
m∠7= 157°
Explanation:
Given that:
m∠8 = 23°
m∠6= 23 ; m∠8 = m∠6 (vertically opposite angles)
m∠5 = m∠7 ( vertically opposite angles)
m∠5 + m∠6 + m∠7 + m∠8 = 360° (sum of angles at a point)
x + 23 + x + 23 = 360
46 + 2x = 360
2x = 360 - 46
2x = 314
x = 314 / 2
x = 157
Hence,
m∠5 = m∠7 = 157°
m∠1 = m∠5 = 157° corresponding angles
m∠4 = m∠8 = 23° corresponding angles
m∠3 = m∠7 = 157° corresponding angles
m∠6 = m∠2 = 23° corresponding angles