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Question
Two lines intersect to form two pairs of vertical angle. <1 with measure (20x+7) and <3 with measure (5x+7y+49) are vertical angles. <2 with measure of (3x-2y+30) and <4 are vertical angles. Find the values of x and y, and the measures/degrees of all four angles.

I know vertical angles are equal to eachother, so I started by setting <1 and <3 equal to eachother and trying to solve for the variables, but I got stuck. As much step-by-step as possible would be appreciated. Please use just fractions, no decimals! Thanks!

Answer
Hello Dakota,

Whatyou did is good, set 20x+7=5x+7y+49, we need one more equation.
We also know <2 (and <4) are supplementary (i.e. form a 180 degree angle)
to <1 and <3....thus, another equation is: 20x+7 + 3x-2y+30 = 180

Solving these for x & y gives: x=7 and y=9.

Thus, <1 = <3 = 147 deg., <2 = <4 = 33 deg.

OK?

Abe  

Algebra

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Abe Mantell

Expertise

Hello, I am a college professor of mathematics and regularly teach all levels from elementary mathematics through differential equations, and would be happy to assist anyone with such questions!

Experience

Over 15 years teaching at the college level.

Organizations
NCTM, NYSMATYC, AMATYC, MAA, NYSUT, AFT.

Education/Credentials
B.S. in Mathematics from Rensselaer Polytechnic Institute
M.S. (and A.B.D.) in Applied Mathematics from SUNY @ Stony Brook

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