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# Algebra/Geometry

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!

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
Questioner's Rating
 Rating(1-10) Knowledgeability = 10 Clarity of Response = 10 Politeness = 10 Comment Really Fantastic Response, Thanks!

Algebra

Volunteer

#### 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