Consider the diagram and angle measures shown below What is the value of m angle 3 ?
1 answer:
Answer:
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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