The internal angles of a triangle in the ratio 3:5:7. Find the degree measures of the angles. Also find measure of its greatest exterior angle.Give complete calculation.

Let 3x be the smallest angle; this will make other angles 5x and 7x.

There are 180° in a triangle, so:

3 x + 5 x + 7 x = 180 °

15 x =180° Divide both sides by 15

x = 180° / 15

x = 12 °

Angles:

3 x = 3 * 12 = 36°

5 x = 5 * 12 = 60°

7 x = 7 * 12 = 84°

Proof:

36° / 84° = 4 * 3 * 3 / ( 4 * 3 * 7 ) = 3 / 7

60 / 84 = 4 * 3 * 5 / ( 4 * 3 * 7 ) = 5 / 7

let the angles be 3x, 5x, and 7x

you know they have to add up to 180°

Solve
3x + 5x + 7x = 180 for x, the sub back into my definitions.

Need to improve in easy way.

Well, let's do some clowny math!

To find the degree measures of the angles, let's assume the ratio 3:5:7 represents the three internal angles of the triangle.

Step 1: Set up the equation

Let the three angles be 3x, 5x, and 7x degrees, respectively.

Step 2: Use the fact that the sum of the internal angles of a triangle is always 180 degrees.

So, we can write the equation:
3x + 5x + 7x = 180

Step 3: Solve the equation

Combine like terms:
15x = 180

Divide both sides by 15:
x = 12

Step 4: Find the degree measures of the angles

Now substitute x back into the original expressions for the angles:
Angle A = 3x = 3 * 12 = 36 degrees
Angle B = 5x = 5 * 12 = 60 degrees
Angle C = 7x = 7 * 12 = 84 degrees

So, the degree measures of the angles are 36 degrees, 60 degrees, and 84 degrees.

Finally, to find the greatest exterior angle of the triangle, we need to know that the sum of an interior and exterior angle is always 180 degrees.

Therefore, the greatest exterior angle would be equal to 180 degrees minus the measure of the smallest interior angle.

The smallest angle is 36 degrees, so the greatest exterior angle would be:
180 - 36 = 144 degrees

Therefore, the greatest exterior angle of the triangle measures 144 degrees.

I hope this math circus performance has brought a smile to your face!

To find the degree measures of the angles of the triangle, we need to determine the multipliers for each ratio.

Let's assign the multipliers as follows:
Internal angle 1: 3x
Internal angle 2: 5x
Internal angle 3: 7x

Since the sum of the internal angles of any triangle is always 180 degrees, we can set up the equation:

3x + 5x + 7x = 180

Simplifying the equation, we get:
15x = 180

Dividing both sides by 15, we find:
x = 12

Now, we can find each internal angle by substituting the value of x:

Internal angle 1: 3x = 3 * 12 = 36 degrees
Internal angle 2: 5x = 5 * 12 = 60 degrees
Internal angle 3: 7x = 7 * 12 = 84 degrees

Therefore, the measures of the internal angles of the triangle are 36 degrees, 60 degrees, and 84 degrees.

To find the measure of the greatest exterior angle of the triangle, we know that the sum of an interior and exterior angle at a vertex on a line is always 180 degrees.

So, the greatest exterior angle is equal to the sum of the other two interior angles. We can find it as:

Greatest exterior angle = 60 degrees + 84 degrees = 144 degrees

Therefore, the measure of the greatest exterior angle of the triangle is 144 degrees.