MHB Finding m<2 When m<1 & m<2 are Given

  • Thread starter Thread starter bernardl
  • Start date Start date
AI Thread Summary
To find m<2 when m<1 and m<2 are given as vertical angles, set the equations equal: 17x + 1 = 20x - 14. Solving for x yields x = 5. Substituting x back into either angle's equation, m<1 or m<2, results in m<2 = 101. Therefore, the measure of angle 2 is 101 degrees.
bernardl
Messages
4
Reaction score
0
<1 and <2 are vertical angles. If m<1 = 17x + 1 and m<2 = 20x - 14, find m<2.
 
Mathematics news on Phys.org
As vertical angles have the same measure, set 17x + 1 = 20x - 14, solve for x and substitute that value for x into the expression for angle 2 (or angle 1 if you prefer; they both have the same measure). The result is the desired measure.
 
Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
Is it possible to arrange six pencils such that each one touches the other five? If so, how? This is an adaption of a Martin Gardner puzzle only I changed it from cigarettes to pencils and left out the clues because PF folks don’t need clues. From the book “My Best Mathematical and Logic Puzzles”. Dover, 1994.
Back
Top