Question

If a || b, m<2 = 63°, and m<9 = 105°, give the measure of each angle.
m<1 =
M<3=
m<4=
m<5=
m<6=
m<7=
m<8=
m<10=
m<11=
m<12=
m<13=
m<14 =

Answer 1

Answer:

a.    m<1 = 105° - 63°                  m<1 = 42°

b. m<3 + m<2 + m<1 = 180°      m<3 = 75°

c. m<4 = m<1                             m<4 = 42°

d. m<5 = m<2                            m<5 = 63°

e. m<6 = m<3                             m<6 = 75°

f. m<7 = m<9                             m<7 = 105°

g. m<8 = m<6                             m<8 = 75°

h. m<10 = m<8                            m<8 = 75°

i. m<11 = m<4                               m<11 = 42°

j. m<12 = 180° - m<11                   m<12 = 138°

k. m<13 = m<11                            m<13 = 42°

l. m<14 = m<12                            m<14 = 138°

Step-by-step explanation:  Sorry if not all are correct

Answer 2

Applying the relationship existing between angle pairs, the measure of each angle in the image are:

m<1 = 42°

m<3 = 75°

m<4 = 42°

m<5 = 63°

m<6 = 75°

m<7 = 105°

m<8 =  75°

m<10 = 75°

m<11 = 42°

m<12 = 138°

m<13 = 42°

m<14 = 138°

Given that a || b, where:

• m<2 = 63°
• m<9 = 105°, the missing angle measures will be determined as follows:

Find m<1:

m<1 + m<2 = m<9 (exterior interior angle theorem)

• Substitute

m<1 + 63° = 105°

m<1 = 105° - 63°

m<1 = 42°

Find m<3:

m<1 + m<2 + m<3 = 180° (angles on a straight line)

• Substitute

42° + 63°+ m<3 = 180°

105° + m<3 = 180°

m<3 = 180° - 105°

m<3 = 75°

Find m<4:

m<4 = m<1 (vertical angles theorem)

• Substitute

m<4 = 42°

Find m<5:

m<5 = m<2 (vertical angles theorem)

• Substitute

m<5 = 63°

Find m<6:

m<6 = m<3 (vertical angles theorem)

• Substitute

m<6 = 75°

Find m<7:

m<7 + m<6 = 180° (corresponding angles theorem)

• Substitute

m<7 + 75° = 180°

m<7 = 180° - 75°

m<7 = 105°

Find m<8:

m<8 = m<6 (alternate interior angles theorem)

• Substitute

m<8 =  75°

Find m<10:

m<10 = m<6 (corresponding angles theorem)

• Substitute

m<10 = 75°

Find m<11:

m<11 = m<4 (alternate interior angles theorem)

• Substitute

m<11 = 42°

Find m<12:

m<12 = m<6 + m<5 (alternate interior angles theorem)

• Substitute

m<12 = 75° + 63°

m<12 = 138°

Find m<13:

m<13 = m<11 (vertical angles theorem)

• Substitute

m<13 = 42°

Find m<13:

m<14 = m<12 (vertical angles theorem)

• Substitute

m<14 = 138°

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