Find the ratio of the interior angles of a triangle if their respective exterior angles are in the ratio of 5:6:7.

well, if the small angle is 5x, then

5x+6x+7x = 180

Now just find x and figure the angles.

Each of 2 two base angles of a triangle is twice of its vertical angle .find the value of the angle of a triangle

To find the ratio of the interior angles of a triangle if their respective exterior angles are in the ratio of 5:6:7, we will first need to understand the relationship between the interior and exterior angles of a triangle.

The exterior angle of a triangle is formed by extending one of its sides. The sum of the measures of the exterior angles of any polygon, including a triangle, is always 360 degrees. In other words, the sum of the measures of the three exterior angles of a triangle is always 360 degrees.

Now, let's find the measures of the individual exterior angles of the triangle. Let's assume that the measures of the three exterior angles are 5x, 6x, and 7x, respectively, where x is a common factor.

Since the sum of the measures of the three exterior angles is 360 degrees, we have the equation: 5x + 6x + 7x = 360.

Simplifying the equation, we get: 18x = 360.

Dividing both sides of the equation by 18, we find that x = 20.

Now that we have found the value of x, we can calculate the measures of the interior angles of the triangle using the formula for the relationship between interior and exterior angles of a triangle, which states that the interior angle and its corresponding exterior angle are supplementary (add up to 180 degrees).

Therefore, the measures of the interior angles of the triangle are:
- First interior angle: 180 - 5x = 180 - 5(20) = 180 - 100 = 80 degrees.
- Second interior angle: 180 - 6x = 180 - 6(20) = 180 - 120 = 60 degrees.
- Third interior angle: 180 - 7x = 180 - 7(20) = 180 - 140 = 40 degrees.

The ratio of the interior angles of the triangle is 80:60:40, which can be simplified to 4:3:2.