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 =
Answers
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
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)
Substitutem<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)
Substitute42° + 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)
Substitutem<4 = 42°
Find m<5:
m<5 = m<2 (vertical angles theorem)
Substitutem<5 = 63°
Find m<6:
m<6 = m<3 (vertical angles theorem)
Substitutem<6 = 75°
Find m<7:
m<7 + m<6 = 180° (corresponding angles theorem)
Substitutem<7 + 75° = 180°
m<7 = 180° - 75°
m<7 = 105°
Find m<8:
m<8 = m<6 (alternate interior angles theorem)
Substitutem<8 = 75°
Find m<10:
m<10 = m<6 (corresponding angles theorem)
Substitutem<10 = 75°
Find m<11:
m<11 = m<4 (alternate interior angles theorem)
Substitutem<11 = 42°
Find m<12:
m<12 = m<6 + m<5 (alternate interior angles theorem)
Substitutem<12 = 75° + 63°
m<12 = 138°
Find m<13:
m<13 = m<11 (vertical angles theorem)
Substitutem<13 = 42°
Find m<13:
m<14 = m<12 (vertical angles theorem)
Substitutem<14 = 138°
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