If m 2 - 98°, m 3 - 23 and m 8 - 70°, find the measure of each missing angle.

Here, we are required to find the value of the other angles in the diagram attached to this answer sheet.

The value of the angles are;

The understanding of the triangle theorem and line theorems is very important to resolve this.

m∠1 + m∠2 = 180° (Theorem: sum of angles on a straight line = 180⁰)

m∠1 + 98 = 180

m∠1 = 180 - 98

m∠2 + m∠3 + m∠7 = 180° (Theorem = sum of angles in a triangle = 180⁰)

98 + 23 + m∠7 = 180

m∠7 + 121 = 180

m∠7 = 180 - 121

m∠4 = m∠7 (Theorem = alternate angles are equal)

m∠6 + m∠7 + m∠8 = 180° (Theorem = sum of angles on a straight line = 180)

m∠6 + 59 + 70 = 180

m∠6 + 129 = 180

m∠6 = 180 - 129

m∠4 + m∠8 + m∠9 = 180° (Theorem = sum of angles in a triangle = 180)

59 + 70 + m∠9 = 180

m∠9 + 129 = 180

m∠9 = 180 - 129

m∠4 + m∠5 = 180° (Theorem = sum of angles on a straight line = 180)

m∠5 + 59 = 180

m∠5 = 180 - 59

m∠10 + m∠9 = 180° (Theorem = sum of angles on a straight line = 180⁰)

m∠10 + 51 = 180

m∠10 = 180 - 51

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The answer is below

Step-by-step explanation:

The complete question is given in the image attached below

m∠1 + m∠2 = 180° (sum of angles on a straight line)

m∠1 + 98 = 180

m∠1 = 180 - 98

m∠1 = 82°

m∠2 + m∠3 + m∠7 = 180° (sum of angles in a triangle)

98 + 23 + m∠7 = 180

m∠7 + 121 = 180

m∠7 = 180 - 121

m∠7 = 59°

m∠4 = m∠7 (alternate angles)

m∠4 = 59°

m∠6 + m∠7 + m∠8 = 180° (sum of angles on a straight line)

m∠6 + 59 + 70 = 180

m∠6 + 129 = 180

m∠6 = 180 - 129

m∠6 = 51°

m∠4 + m∠8 + m∠9 = 180° (sum of angles in a triangle)

59 + 70 + m∠9 = 180

m∠9 + 129 = 180

m∠9 = 180 - 129

m∠9 = 51°

m∠4 + m∠5 = 180° (sum of angles on a straight line)

m∠5 + 59 = 180

m∠5 = 180 - 59

m∠5 = 121°

m∠10 + m∠9 = 180° (sum of angles on a straight line)

m∠10 + 51 = 180

m∠10 = 180 - 51

m∠10 = 129°

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