If m∠8=23°, find the measure of each missing angle. give your reasoning.
m∠1=?
m∠2=?
m∠3=?
m∠4=?
m∠5=?
m∠6=?
m∠7=?

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°

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Step-by-step explanation:

two lines are parallel and another line is a transverse.

Given m∠8 = 23°

a). Since m∠1 + m∠4 = 180°[Supplementary angles]

and m∠4 = m∠8 [Corresponding angles]

Therefore, m∠1 + m∠8 = 180°

m∠1 = 180° - m∠8

       = 180°- m∠8

       = 180 - 23

       = 157°

b). Since m∠2 = m∠6 [Corresponding angles]

and m∠6 = m∠8 [Vertically opposite angle]

therefore, m∠2 = m∠8 = 23°

c). Since m∠3 = m∠1 [vertically opposite angles]

Therefore, m∠3 = 153°

d). Since m∠4 = m∠2 [vertically opposite angles]

therefore, m∠4 = 23°

e). Since m∠5 = 180 - m∠4 [interior angles]

m∠5 = 180 - 23

        = 157°

f). Since m∠6 = m∠8 [Vertically opposite angles]

Therefore, m∠6 = 23°

g). Since m∠7 = 180 - m∠6 [supplementary angles]

m∠7 = 180 - 23

        = 157°

the 2 figures are congruent bc if you reflect abcd over the y axis then over the d axis the figures overlap

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