Consider the diagram and angle measures shown below What is the value of m angle 3 ?

The answer is below

Step-by-step explanation:

m∠lon = m∠2 (vertical opposite angles are equal)

m∠lon = m∠1 (corresponding angles are equal).

Therefore; m∠2 = m∠1 (substitution property)

3x + 25 = 7x + 5

Subtracting 5 and 3x from both sides of the equation:

3x + 25 - 5 - 3x = 7x + 5 - 5 - 3x

4x = 20

dividing through by 4:

4x / 4 = 20 / 4

x = 5

Given that:

m∠3 = -2x + 70

substituting x = 5:

m∠3 = -2(5) + 70 = 60

m∠3 = 60°

Therefore:

m∠4 + m∠2 + m∠3 = 180° (substitution)

(155 - 3x) + (7x + 5) + (-2x + 70) = 180

(-3x + 7x - 2x) + (155 + 5 + 70) = 180

2x + 230 = 180

2x = -50

x = -25

Therefore; m∠3 = -2x + 70 = -2(-25) + 70 = 50 + 70

m∠3 = 120°

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