The second angle of a triangle is 3 times as large as the first. the third angle is 50° more than the first. find the measure of the smallest angle

Your smallest angle is 26°

Angles in a triangle add up to 180°. This means:

Angle1 + Angle2 + Angle3 = 180°

The second angle of a triangle is 3 times as large as the first.

Angle2 = 3 * Angle1

The third angle is 50° more than the first.

Angle3 = Angle1 + 50°

Substitute these into the first formula, in terms of Angle1.

Angle1 + (3 * Angle1) + (Angle1 + 50°) = 180°

Expand and simplify.

5 * Angle1 + 50° = 180°

Put it into the formula Ax = B. You will have all the variables on one side and the integers on the other.

5 * Angle1 + 50° = 180°

5 * Angle1 + 50° - 50° = 180° - 50°

5 * Angle1 = 130°

Put it into the formula x = b. Solve to find 1 of the variable.

5 * Angle1 = 130°

5 * Angle1 / 5 = 130° / 5

Angle1 = 26°

Check this is right by substituting into the given formulas.

Angle2 = 3 * Angle1

Angle2 = 3 * 26

78 = 3 * 26

Angle3 = Angle1 + 50°

Angle3 = 26 + 50°

76 = 26 + 50°

Angle1 + Angle2 + Angle3 = 180°

26 + 78 + 76 = 180°