A triangle has angles described as followed: the first angle is four more than seven times a number, another angle is four less than the first and the third angle is twice as large as the first. What are the sizes of each angle.
I got the first angle of the triangle but I am having trouble what the expression is for angle 2 and 3..
if the three angles are x,y,z, then
x = 7n+4
y = x-4
z = 2x
So, how did you get a value for x and not be able to come up with y and z? They have to add to 180 degrees.
By the way, what did you get for x?
To find the expressions for the second and third angles, let's first assign a variable to the unknown number mentioned in the problem. Let's call it "x".
Given that the first angle is four more than seven times x, we can express it as:
First angle = 7x + 4
Now, according to the problem, the second angle is four less than the first angle. So we can write it as:
Second angle = (First angle) - 4
Substituting the expression we found for the first angle:
Second angle = (7x + 4) - 4
Simplifying:
Second angle = 7x
Lastly, we are given that the third angle is twice as large as the first angle. Therefore:
Third angle = 2 * (First angle)
Substituting the expression for the first angle:
Third angle = 2 * (7x + 4)
Simplifying:
Third angle = 14x + 8
So, the expressions for the second and third angles are:
Second angle = 7x
Third angle = 14x + 8