The degree measures of the angles of the triangle are in the ratio 4: 5: 6. Find the degree measure

The degree measures of the angles of the triangle are in the ratio 4: 5: 6. Find the degree measure of the smallest of the angles.

1. Vertices of the triangle – A, B, C.

2. Suppose ∠А: ∠В: ∠С = 4: 5: 6.

3. We take as x the number of degrees per part.

4. We draw up an equation, taking into account that the total value of the interior angles of the triangle is 180 °:

4x + 5x + 6x = 180 °;

15x = 180 °; x = 12 °.

5. We calculate the value of the degree measures of the angles of the triangle ABC:

∠A = 4 x 12 = 48 °.

∠B = 5 x 12 = 60 °.

∠C = 6 x 12 = 72 °.

The smallest of them is ∠A.

Answer: ∠А = 48 ° – the smallest of all the interior angles of the triangle ABC.