Respuesta :
Answer:
Therefore m angle 2 is 86°.
Step-by-step explanation:
Given:
m∠ 1 = 17x + 1
m∠ 2 = 20x - 14
To Find:
m∠ 2 =?
Solution:
Vertical Angles:
The angles opposite each other when two lines cross. They are always equal.
∴ m∠ 1 = m∠ 2
Substituting the given values we get
[tex]17x+1=20x-14\\\\20x-17x=1+14\\\\3x=15\\\therefore x=\dfrac{15}{3}=5[/tex]
Now for m∠ 2
[tex]\angle 2=20\times 5-14=100-14=86\°[/tex]
Therefore m angle 2 is 86°.
m<2 = 86°
Vertical angles are always congruent
m<1 = 17x + 1
m<2 = 20x - 14
Since <1 and <2 are vertical:
m<1 = m<2
17x + 1 = 20x - 14
Collect like terms
20x - 17x = 1 + 14
3x = 15
Divide both sides by 3
3x / 3 = 15/3
x = 5
m<2 = 20x - 14
m<2 = 20(5) - 14
m<2 = 100 - 14
m<2 = 86°
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