In a triangle ABC, angle B is three times angle A and angle C is 5 degrees less than 6 times angle A. Find the size of the angles.
B = 3A
C = 6A -5
Since triangles have 180 degrees:
A + 3A + 6A - 5 = 180
Solve for A and then insert that value into the first two equations to solve for b and C.
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To solve this problem, let's use variables to represent the angles in the triangle.
Let's say angle A = x degrees.
Since angle B is three times angle A, we can write angle B = 3x degrees.
And since angle C is 5 degrees less than 6 times angle A, we can write angle C = (6x - 5) degrees.
Now, we know that the sum of the angles in a triangle is always 180 degrees.
So, we can write the equation:
x + 3x + (6x - 5) = 180
Simplifying the equation, we get:
10x - 5 = 180
Adding 5 to both sides:
10x = 185
Dividing both sides by 10:
x = 18.5
Now that we have the value of x, we can substitute it back into our equations to find the values of angles A, B, and C.
Angle A = x = 18.5 degrees
Angle B = 3x = 3 * 18.5 = 55.5 degrees
Angle C = 6x - 5 = 6 * 18.5 - 5 = 108 - 5 = 103 degrees
So, the sizes of the angles in the triangle are:
Angle A = 18.5 degrees
Angle B = 55.5 degrees
Angle C = 103 degrees