Answer/Step-by-step explanation:
Given that m<3 = 54°
a. <1, <2, and <3 are angles on a straight line. They add up to 180°.
m<3 is given as 54°, m<2 = 90°, therefore,
m<1 = 180 - (54 + 90) = 180 - 144
m<1 = 36°
b. <2 is indicated as a right angle. Therefore, m<2 = 90°
c. <1 and <4 are vertical opposite angles. Vertical angles are congruent, since m<1 = 36°, therefore, m<4 = 36°
d. <5 and <2 are vertical opposite angles. m<2 = m<5, therefore, m<5 = 90°
e. <6 and <3 are vertical opposite angles. m<3 = m<6, therefore, m<6 = 54°
f. m<7 + m<6 = 180° (same side interior angles are supplementary)
m<7 = 180 - m<6
m<7 = 180 - 54
m<7 = 126°
g. m<7 + m<8 = 180° (linear pair)
126° + m<8 = 180
m<8 = 180 - 126
m<8 = 54°
h. m<9 = 180 - m<8 (linear pair)
m<9 = 180 - 54
m<9 = 126°
i. m<10 = m<8 (vertical angles)
m<10 = 54°
j. m<11 = m<4 (alternate interior angles are congruent)
m<11 = 36°
k. m<12 = 180 - m<11 (linear pair)
m<12 = 180 - 36
m<12 = 144°
l. m<13 = m<11 (vertical angles)
m<13 = 36°
m. m<14 = m<12 (vertical angles)
m<14 = 144°
