Question

If m∠2 = 41°, m∠5 = 94°, and m∠10 = 109°, find each measure.

Answer 1

Answer:

Step-by-step explanation:

It's given in this question,

m∠2 = 41°, m∠5 = 94° and m∠10 = 109°

Since, ∠2 ≅ ∠9 [Alternate interior angles]

m∠2 = m∠9 = 41°

m∠8 + m∠9 + m∠10 = 180° [Sum of angles at a point of a line]

m∠8 + 41 + 109 = 180

m∠8 = 180 - 150

m∠8 = 30°

Since, m∠2 + m∠7 + m∠8 = 180° [Sum of interior angles of a triangle]

41 + m∠7 + 30 = 180

m∠7 = 180 - 71

m∠7 = 109°

m∠6 + m∠7 = 180° [linear pair of angles]

m∠6 + 109 = 180

m∠6 = 180 - 109

        = 71°

Since m∠5 + m∠4 = 180° [linear pair of angles]

m∠4 + 94 = 180

m∠4 = 180 - 94

m∠4 = 86°

Since, m∠4 + m∠3 + m∠9 = 180° [Sum of interior angles of a triangle]

86 + m∠3 + 41 = 180

m∠3 = 180 - 127

m∠3 = 53°

m∠1 + m∠2 + m∠3 = 180° [Angles on a point of a line]

m∠1 + 41 + 53 = 180

m∠1 = 180 - 94

m∠1 = 86°

Answer 2

From the information and diagram shown, the following are true;

• m<2 = m<9

Since m<2 is 41 degrees, hence m<9 is 41 degrees

Also, m<7 = m<10 (corresponding angles) =109 degreees

m<6 + m<7 = 180

m<6 = 180 - 109

m<6 = 71 degrees

m<4 + m<5 = 180

m<4 = 180 - 94

m<4 = 86 degrees

m<1 = m<4 (corresponding angles) = 86 degrees

m<8 + m<2 + m<7 = 180

m<8 + 41 + 109 = 180

m<8 = 180 - 150

m<8 = 30degrees

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