Given m<12 =121 and m<6 =75 find the measure of the missing angles

a. m∠1 = 75°

b. m∠2 = 46°

c. m∠3 = 59°

d. m∠4 = 59°

e. m∠5 = 46°

f. m∠7 = 121°

g. m∠8 = 59°

h. m∠9 = 62°

i. m∠10 = 118°

j. m∠11 = 59°

k. m∠13 = 118°

i. m∠14 = 62°5

Example 5

m∠1 =78°

m∠2 = 102°

m∠3 = 59°

m∠4 = 102°

m∠5 =  38

m∠6 = 142°

m∠7 = 38°

m∠8 = 142°

m∠9 = 78°

m∠11 = 78°

m∠12 =  102°

m∠13 = 38°

m∠14 =  142°

Step-by-step explanation:

a. m∠1 ≅ m∠6 (Alternate angle theorem)

m∠1 = m∠6 = 75° (Definition of congruency)

m∠1 = 75°

b. m∠12 = m∠5 + m∠6 (Angle addition postulate/Corresponding angles)

m∠5 = 121° - 75° = 46°

m∠5 = 46°

m∠2 ≅ m∠5 (Alternate angle theorem)

m∠2 = m∠5 = 46° (Definition of congruency)

m∠2 = 46°

c. m∠3 = 180 - (m∠1 + m∠2) (Angle subtraction and sum of angles on a straight line)

m∠3 = 180 - (75 + 46) = 59°

m∠3 = 59°

d. m∠4 = 180 - (m∠1 + m∠5)

m∠4 = 180 - (75 + 46) = 59°

m∠4 = 59°

e. m∠12 = m∠5 + m∠6 (Angle addition postulate/Corresponding angles)

m∠5 = 121° - 75° = 46°

m∠5 = 46°

f. m∠7 = m∠12 = 121° (Alternate angle theorem)

m∠7 = 121°

g. m∠8 = 180 - m∠7 = 180 - 121 = 59°

m∠8 = 59°

h. m∠9 + m∠5 + m∠8 = 180 (The sum of the interior angles of a triangle)

m∠9 = 180 - (59 + 59) = 62°

m∠9 = 62°

i. m∠10 = 180 - m∠9 = 180 - 62 = 118°

m∠10 = 118°

j. m∠11 = m∠8 = 59°

m∠11 = 59°

k. m∠13 = m∠10 = 118°

m∠13 = 118°

i. m∠14 = m∠9 = 62°

m∠14 = 62°

Example 5

m∠5 = m∠7 = 38

m∠5 =  38°

m∠6 = 180 - 38 = 142°

m∠6 = 142°

m∠8 = m∠6 = 142°

m∠8 = 142°

m∠12 = m∠10 = 102°

m∠12 =  102°

m∠11 = 180 - m∠12 = 180 - 102 = 78°

m∠11 = 78°

m∠9 = m∠11 = 78°

m∠9 = 78°

m∠1 = m∠9 = 78°

m∠1 =78°

m∠3 = 78°

m∠2 = m∠4 = m∠10 = 102°

m∠13 = 360 - (m∠3 + m∠6 + m∠12) = 360 - (78 + 142 + 102) = 38°

m∠13 = 38°

m∠15 = 38°

m∠14 = m∠16 = 180 - m∠15 = 180 - 38° = 142°

m∠14 =  142°

m∠16 = 142°

54

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