Angle 1 and angle 2 are vertical angles if m angle 1 = 17x+1 and m angle 2 = 20x-14 find m angle 2

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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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

Now for m∠ 2  

Therefore m angle 2 is 86°.