In the triangle ABC, angle ABC is x, angle BCA is x+40, and angle CAB is 2x. What is the measure of the largest angle (in degrees) ?
To find the measure of the largest angle, we need to determine the values of x, x+40, and 2x.
We know that the sum of the angles in a triangle is 180 degrees. So we can set up the equation:
x + (x + 40) + 2x = 180
Combining like terms, we get:
4x + 40 = 180
Subtracting 40 from both sides:
4x = 140
Dividing both sides by 4, we find:
x = 35
Now we can determine the values of each angle:
Angle ABC = x = 35 degrees
Angle BCA = x + 40 = 35 + 40 = 75 degrees
Angle CAB = 2x = 2(35) = 70 degrees
Therefore, the largest angle is angle BCA, which measures 75 degrees.
To find the measure of the largest angle in triangle ABC, we need to solve for the value of x.
In any triangle, the sum of all the angles is always 180 degrees. So we can use this information to set up an equation:
x + (x + 40) + 2x = 180
Simplifying the equation, we get:
4x + 40 = 180
Next, we can solve for x by subtracting 40 from both sides of the equation:
4x = 140
Dividing both sides by 4, we find:
x = 35
Now that we have the value of x, we can substitute it back into one of the angle expressions to find the measure of the largest angle. Since angle CAB is given in terms of x, we can use that expression:
angle CAB = 2x = 2 * 35 = 70 degrees
Therefore, the measure of the largest angle in triangle ABC is 70 degrees.
A = 2X, B = X, C = (X + 40).
A + B + C = 180 deg.
2x + x + (x + 40) = 180,
4x + 40 = 180,
4x = 180 - 40,
4x = 140,
x = B = 140 / 4 = 35 deg.
2X = A = 2*35 = 70 deg.
(x + 40) = C = 35 + 40 = 75 deg = Largest angle.