The angles in a triangle are such that one angle is 102∘ more than the smallest angle, while the third angle is 4 times as large as the smallest angle. Find the measures of all three angles.

Answer:13 degrees, 115 degrees, and 52 degreesStep-by-step explanation:The addition of the three internal angles in a triangle should give 180 degrees.So let's name the angles A, B, C, with:A being the smallest angleB being the one that equals the smallest one plus 102 degrees. That is: B = A+102C being the one that is 4 times the smallest one. That is: C = 4 * ANow add the three to obtain 180, but writing all of them in terms of the smallest angle A:A + A + 102 +4 A = 1802A + 4A + 102 = 1806 A + 102 = 1806 A = 180 -102 = 78A = 78/6 = 13 degreesTherefore, angle B must be: A + 102 = 13 +102 = 115 degreesC = 4 * A = 4 * 13 = 52 degrees