The measure of each angle and their reasoning are explained for all in the explanation below.
We are given that;
m∠8=23°
a). From the given image, we see that;
m∠1 and m∠8 are supplementary angles and as such they sum up to 180°;
Thus; m∠1 + m∠8 = 180°
m∠1 = 180° - m∠8
m∠1 = 180 - 23
m∠1 = 157°
b). We see that m∠1 and m∠2 are angles that form a straight line.
Sum of angles on a straight line equals 180°. Thus;
m∠1 + m∠2 = 180°
m∠2 = 180 - 157
m∠2 = 23°
c). We see that m∠3 and m∠1 are vertically opposite angles and they must be equal. Thus
m∠3 = m∠1
Thus; m∠3 = 153°
d). We see that m∠4 and m∠2 are vertically opposite angles and they must be equal. Thus
m∠4 = m∠2
Thus; m∠4 = 23°
e). We see that m∠5 and m∠1 are corresponding angles and are therefore equal. Thus;
m∠5 = m∠1
m∠5 = 157°
f). We see that m∠6 and m∠8 are vertically opposite angles and as such;
m∠6 = m∠8
Thus, m∠6 = 23°
g). We see that m∠7 and m∠5 are vertically opposite angles and are therefore equal. Thus;
m∠5 = m∠7
m∠5 = 157°
