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.

13 degrees, 115 degrees, and 52 degrees

Step-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 angle

B being the one that equals the smallest one plus 102 degrees. That is: B = A+102

C being the one that is 4 times the smallest one. That is: C = 4 * A

Now add the three to obtain 180, but writing all of them in terms of the smallest angle A:

A + A + 102 + 4 A = 180

2A + 4A + 102 = 180

6 A + 102 = 180

6 A = 180 - 102 = 78

A = 78/6 = 13 degrees

Therefore, angle B must be: A + 102 = 13 + 102 = 115 degrees

C = 4 * A = 4 * 13 = 52 degrees