In triangle ABC, angle B = 3, angle A and angle C = 8 angle A. How many degrees are there in angle B ?

a. 15 degree
b. 30 degree
c. 45 degree
d. 60 degree
e. 120 degree

please answer and explain

the sum of the angles in a triangle is 180 degrees.

A+3A+8A=180
12A=180
A=15

B=3A=45 deg

To find the value of angle B in triangle ABC, we need to use the fact that the sum of all angles in a triangle is always 180 degrees. Let's break down the problem step by step:

Let's assume the value of angle A is "x" degrees.
Since angle C is 8 times angle A, we can express angle C as 8x degrees.

According to the given information, angle B is 3 degrees. We need to find the value of angle B in degrees.

Now, we can use the fact that the sum of all angles in a triangle is 180 degrees:

x + 3 + 8x = 180

Combining like terms, we have:

9x + 3 = 180

Next, we subtract 3 from both sides to isolate the variable:

9x = 177

Finally, we divide both sides by 9 to solve for x:

x = 177/9
x ≈ 19.67

Now, we can substitute the value of x back into the expression for angle C:

angle C = 8x ≈ 8 * 19.67 ≈ 157.33 degrees

Therefore, angle C is approximately 157.33 degrees.

Since the question asks for the value of angle B, we can subtract angles A, B, and C from 180 degrees:

Angle B = 180 - angle A - angle C
Angle B = 180 - 19.67 - 157.33
Angle B ≈ 3

Therefore, the value of angle B is approximately 3 degrees.

Considering the answer choices provided,
the correct answer is a. 15 degrees.
This is the closest option to the approximate value we calculated.