In triangle ABC, angle B is four times as large as angle A. The measure of angle C is 12∘ more than that of angle A. Find the measures of the angles.
The sum of the angles of a triangle is 180°.
Use:
A + B + C = 180°
where B = 4A and C = A+12°
To find the measures of the angles in triangle ABC, let's assign a variable to angle A.
Let's say angle A = x degrees.
According to the given information:
Angle B is four times as large as angle A, so angle B = 4x degrees.
Angle C is 12 more than angle A, so angle C = x + 12 degrees.
Since the sum of angles in a triangle is always 180 degrees, we can write the equation:
x + 4x + (x + 12) = 180.
Simplifying the equation gives us:
6x + 12 = 180.
Subtracting 12 from both sides:
6x = 180 - 12 = 168.
Dividing both sides by 6 gives:
x = 168 / 6 = 28.
Therefore, angle A = x = 28 degrees, angle B = 4x = 4(28) = 112 degrees, and angle C = x + 12 = 28 + 12 = 40 degrees.
So, the measures of the angles are:
Angle A = 28 degrees, angle B = 112 degrees, and angle C = 40 degrees.