The exterior angle measures 6 degrees.
In triangle ABC, let ∠ABC be y degrees, and ∠BCA be (2x + 18) degrees.
The exterior angle, BAM, is given as (3x + 6) degrees.
According to the Exterior Angle Theorem, the measure of the exterior angle (BAM) is equal to the sum of the measures of the two remote interior angles (ABC and BCA).
Therefore, (3x + 6) degrees is equal to (y + (2x + 18)) degrees.
Equating the expressions, we have:
3x + 6 = y + 2x + 18
Solving for \(y\), we get:
y = x - 12
Now, to find the measure of the exterior angle, substitute y back into the expression 3x + 6:
3x + 6 = 3x + 6 - 12 + 6
Simplifying, we get:
3x + 6 = 3x
The constant terms cancel out, leaving 3x = 3x, which is true for all values of x.
Therefore, the measure of the exterior angle is 3x + 6, and it is independent of the value of x.
The exterior angle measures 6 degrees.
The probable question may be:
In triangle ABC, Angle ABC is degree, Angle BCA is ( 2x+ 18)degree. the line is drawn from point A to point M outward which is an exterior angle. as BAM is (3x+6) degree.
Find the measure of exterior angle of triangle.