in triangle ABC, the size of angle B is 5 times the size of angle A and the size of angle C is 9 degrees less than 4 times the size of angle A

Question

Find the size of angle A

Answer 1

You can set up the equations as follows:
B=5A
C=4A-9
A+B+C=180 (sum of angles of a triangle).
and solve for A, B and C.

However, you can easily solve it by substitution into the third equation:
A+B+C=180
A + 5A + 4A-9 = 180
10A=189
A=18.9
With A known, you can then find the remaining angles by substitution into the first two equation.

Answer 2

The sum of the angles of a triangle are 180 degrees.

Therefore:
Let x = angle A
5x = angle B
4x - 9 = angle C

Equation:
x + 5x + 4x - 9 = 180

Solve for x.