Question

If m∠3 = 54°, find the measure of each missing angle.

Answer 1

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°