In a triangle ABC , angle B is 4 times angle A and angle C is 17 degrees less than 5 times angle A. Find the size of the angles.

B=4A

C=5A-17

The three angles of a triangle add up to 180 degrees.

A+B+C=180

hint: use substitution.

21.88888

To solve this problem, we can let the measure of angle A be represented by x degrees. Then, we can use the given information to express the measures of angles B and C in terms of x.

Given:
Angle B is 4 times angle A, so angle B = 4x degrees.
Angle C is 17 degrees less than 5 times angle A, so angle C = (5x - 17) degrees.

In any triangle, the sum of the angles is always 180 degrees. Therefore, we can write the equation:

x + 4x + (5x - 17) = 180

Simplifying the equation, we have:
10x - 17 = 180

Adding 17 to both sides of the equation, we have:
10x = 197

Dividing both sides of the equation by 10, we have:
x = 19.7

Now, we can substitute the value of x into the expressions for angles B and C to find their measures.

Angle B = 4x = 4 * 19.7 = 78.8 degrees
Angle C = 5x - 17 = 5 * 19.7 - 17 = 98.5 - 17 = 81.5 degrees

Therefore, the measures of the angles are:
Angle A = 19.7 degrees
Angle B = 78.8 degrees
Angle C = 81.5 degrees