# SOLUTION: in a hexagon three angles have the same measure. The measure of each of the congruent angles is twice the measure of the fourth angle and is half the measure of the fifth angle. Th

Algebra ->  Algebra  -> Triangles -> SOLUTION: in a hexagon three angles have the same measure. The measure of each of the congruent angles is twice the measure of the fourth angle and is half the measure of the fifth angle. Th      Log On

 Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations! Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!

 Geometry: Triangles Solvers Lessons Answers archive Quiz In Depth

 Click here to see ALL problems on Triangles Question 173993: in a hexagon three angles have the same measure. The measure of each of the congruent angles is twice the measure of the fourth angle and is half the measure of the fifth angle. The sixth angle measures 115. What is the measure of the smallest angle?Answer by gonzo(654)   (Show Source): You can put this solution on YOUR website!a hexagon has 6 angles. the total number of internal degrees is (n-2)*180 = 4*180 = 720 degrees. ----- let a = one of the congruent angles. you have: angles 1, 2, and 3 = a. ----- if a = 2 * angle 4, then angle 4 = 1/2 * a ----- if a = 1/2 * angle 5, then angle 5 = 2 * a ----- we have: angle 1 = a angle 2 = a angle 3 = a angle 4 = 1/2 * a angle 5 = 2 * a angle 6 = 115 ----- since the sum of the angles is equal to 720, we have: 3*a + 2*a + 1/2*a + 115 = 720 combine like terms to get: 5.5 * a + 115 = 720 subtract 115 from both sides to get: 5.5 * a = 720 - 115 = 605 divide both sides by 5.5 to get: a = 720/5.5 = 110 ----- angle 1, 2, and 3 are each 110 degrees. angle 4 = 55 degrees angle 5 = 220 degrees angle 6 = 115 degrees ----- the question is: What is the measure of the smallest angle? the answer is: 55 degrees.