the interior angle measures of a triangle are in 3:8:9 what is the measure of this triangles largest interior angle

9/20 = x/180

20x = 1,620

x = 81

To find the measure of the largest interior angle of the triangle, we first need to determine the values of the three interior angles.

Let's represent the measures of the interior angles by 3x, 8x, and 9x. Since the sum of the interior angles in a triangle is always 180 degrees, we can set up the following equation:

3x + 8x + 9x = 180

Combining like terms, we get:

20x = 180

Now, we can solve for x by dividing both sides of the equation by 20:

x = 180/20 = 9

To find the measure of the largest interior angle, we substitute the value of x back into the equation:

9x = 9 * 9 = 81

Therefore, the measure of the largest interior angle of the triangle is 81 degrees.

To find the measure of the largest interior angle of a triangle when the interior angle measures are given in a ratio, you need to follow these steps:

Step 1: Determine the sum of the interior angles of a triangle, which is always 180 degrees.

Step 2: Write the ratio of the given interior angle measures as 3x:8x:9x, where x is a common factor for all three measures.

Step 3: Add the three measures together and set it equal to 180 degrees, as the sum of the interior angles of a triangle is always 180:

3x + 8x + 9x = 180

Step 4: Simplify the equation by combining like terms:

20x = 180

Step 5: Solve for x by dividing both sides of the equation by 20:

x = 180 / 20
x = 9

Step 6: Substitute the value of x back into the ratio to find the measure of each angle:

Largest interior angle = 9x = 9 * 9 = 81 degrees

Therefore, the measure of the largest interior angle of the triangle is 81 degrees.