Question 1052633
<font color=black size=3>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</font>