Question

In a triangle one interior angle is 58° blgger than the original interior angle. The third

angle is 37 larger than three times the original interlor angle.

Answer 1

The question involves solving for the angles in a triangle, given that one angle is 58° larger than the first and the third is 37° larger than three times the first. By setting up an equation with the sum of angles equal to 180°, the original angle is calculated to be 17°.

Step-by-step explanation:

The subject matter of the question is Mathematics, specifically involving the properties of triangles. When considering a triangle, it is a basic rule that the sum of the interior angles must equal 180 degrees. Let's denote the original interior angle as x. According to the question, one angle is 58° larger than x, hence, that angle is x + 58°. The third angle is described as being 37° larger than three times the original angle, which makes it 3x + 37°. Putting these together in an equation based on the sum of a triangle's interior angles we get:

x + (x + 58) + (3x + 37) = 180

Combining like terms:

5x + 95 = 180

Now we will solve for x by subtracting 95 from both sides of the equation:

5x = 85

And then dividing by 5:

x = 17°

Thus, the original angle is 17°, the second angle is 17° + 58° = 75°, and the third angle is 3(17°) + 37° = 88°.