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°

constant acceleration- a

constant velocity- c

no velocity or acceleration- b

explanation:

for body moving with a constant acceleration, the rate of change of displacement changes over time. this is proven by the increasing gradient of the curve (a) against time.

a body that is moving at constant velocity covers equal distances over equal periods of time, thus the straight line with a constant gradient c.

a stationary body   covers no displacement as time elapses. thus the flat line with   zero gradient.

stops on an even number.