In triangle ABC, the size of angle B is 5 times the size of angle A, and the size of Angle c is 15 degrees less than 4 times the size of angle A. What is the size of angle A? What is the size of angle B? What is the size of angle C?
A+B+C = 180 for a triangle ABC
B = 5A
C = 4A-15
A + 5A + 4A - 15 = 180
10A = 195
A = 19.5
B = 97.5
C = 63
Let's assume the size of angle A is represented by 'x' degrees.
Angle B is given as 5 times the size of angle A, so angle B = 5x degrees.
Angle C is given as 15 degrees less than 4 times the size of angle A, so angle C = (4x - 15) degrees.
To find the size of angle A, we need to solve the equation:
A + B + C = 180 degrees (because the sum of the angles in a triangle is 180 degrees)
Substituting the values we have:
x + 5x + (4x - 15) = 180
Simplifying the equation:
10x - 15 = 180
Adding 15 to both sides:
10x = 195
Dividing both sides by 10:
x = 19.5
Therefore, the size of angle A is 19.5 degrees.
Angle B = 5x = 5 * 19.5 = 97.5 degrees.
Angle C = (4x - 15) = (4 * 19.5 - 15) = 78 - 15 = 63 degrees.
So, the size of angle A is 19.5 degrees, the size of angle B is 97.5 degrees, and the size of angle C is 63 degrees.
To find the sizes of the angles in triangle ABC, we can use the information given.
Let's denote the size of angle A as x degrees.
According to the given information:
- The size of angle B is 5 times the size of angle A, so angle B = 5x degrees.
- The size of angle C is 15 degrees less than 4 times the size of angle A, so angle C = (4x - 15) degrees.
Now, we can find the values of angle A, angle B, and angle C.
Angle A = x degrees (as given)
Angle B = 5x degrees (since angle B is 5 times angle A)
Angle C = (4x - 15) degrees (since angle C is 15 degrees less than 4 times angle A)
So, the sizes of the angles in triangle ABC are as follows:
- Angle A is x degrees.
- Angle B is 5x degrees.
- Angle C is (4x - 15) degrees.