Hi I need help with this problem full solution only please: Two angles of a triangle have the same measure and the third one is 9 degrees greater than the measure of each of the other two. Find the measure of the LARGEST angle in the triangle.
in a triangle the sum of all angles = 180
ie., x+y+z=180 -(1)
suppose y=z
and x= 9+y or 9+z
ie.,
than (1) becomes
9+y+y+z=180
as y=z
9+y+y+y=180
9+3y=180
3y=180-9
y=180-9/3
there u get y put in x= 9+y u get the largest angle x
Angle #1 = X Deg.
Angle #2 = X Deg.
Angle #3 = (X+9) Deg.
x + x + x+9 = 180 Deg.
3x = 171.
X = 57o
x+9 = 57+9 = 66o = Largest angle.
To solve this problem, let's assign variables to the angles of the triangle.
Let's say the measure of the two angles that are the same is x degrees.
According to the problem, the third angle is 9 degrees greater than each of the other two angles. So the measure of the third angle can be expressed as x + 9 degrees.
Now, we know that the sum of all angles in a triangle is always 180 degrees.
So, we can set up the following equation:
x + x + (x + 9) = 180
Let's simplify the equation:
3x + 9 = 180
Subtract 9 from both sides:
3x = 171
Now, divide both sides by 3:
x = 57
So, the measure of each of the two angles that are the same is 57 degrees.
Now, let's find the measure of the largest angle in the triangle.
We can substitute the value of x into one of the expressions we found earlier:
57 + 9 = 66
Therefore, the measure of the largest angle in the triangle is 66 degrees.