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.
x + x + x+9 = 180
all yours ...
is the answer 57?
Let's denote the measure of the two equal angles as x degrees. Therefore, the measure of the third angle is (x + 9) degrees.
The sum of the angles in a triangle is always 180 degrees. We can use this information to set up an equation:
x + x + (x + 9) = 180
Combining like terms, we get:
3x + 9 = 180
Subtracting 9 from both sides, we have:
3x = 171
Dividing both sides by 3, we find:
x = 57
Now we can substitute this value back into the expression for the third angle:
x + 9 = 57 + 9 = 66
Therefore, the largest angle in the triangle measures 66 degrees.
To find the measure of the largest angle in the triangle, let's assign variables to represent the measures of the angles.
Let the measure of the first two angles be x, and the measure of the third angle (the largest one) be x + 9.
We know that the sum of the angles in a triangle is always 180 degrees.
Therefore, we can set up an equation:
x + x + (x + 9) = 180
Combining like terms, we have:
3x + 9 = 180
Now, let's solve for x:
3x = 180 - 9
3x = 171
Dividing both sides by 3:
x = 171 / 3
x = 57
Now that we have the value of x, we can find the measure of the largest angle (x + 9):
x + 9 = 57 + 9
x + 9 = 66
Therefore, the measure of the largest angle in the triangle is 66 degrees.