SOLUTION: <1 and <2 are vertical angles. Find the measure of each angle. m<1= 2x+10, m<2= 3x-40.

Algebra ->  Angles -> SOLUTION: <1 and <2 are vertical angles. Find the measure of each angle. m<1= 2x+10, m<2= 3x-40.      Log On


   

Question 1052633: <1 and <2 are vertical angles. Find the measure of each angle. m<1= 2x+10, m<2= 3x-40.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Rule: Vertical angles are congruent (i.e. equal)


Since angle 1 and angle 2 are congruent, this means that the measures of the angles are equal.


m < 1 = m < 2


2x+10 = 3x-40


2x+10-2x = 3x-40-2x


10 = x-40


10+40 = x-40+40


50 = x


x = 50


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Now let's use the value of x to find the measure of each angle


m < 1 = 2x+10


m < 1 = 2*50+10


m < 1 = 100+10


m < 1 = 110


Angle 1 is 110 degrees.


Angle 2 is also 110 degrees. Notice how plugging x = 50 into the other equation also yields 110


m < 2 = 3x-40


m < 2 = 3*50-40


m < 2 = 150-40


m < 2 = 110


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Final Answers:


Angle 1 is 110 degrees. Angle 2 is 110 degrees