the sum of the measures of the angles of any triangle is 180 degrees . in triangle ABC, angles A and B have the same measure , while the measure of angle C is 84 degrees larger than each A and B. what are the measures of the three angles ?
Let x be the measure of angle A and angle B.
Since angles A and B have the same measure, angle A = angle B = x.
The measure of angle C is 84 degrees larger than each angle A and B, so angle C = x + 84.
According to the fact that the sum of the measures of the angles of any triangle is 180 degrees, we have:
x + x + (x + 84) = 180
3x + 84 = 180
3x = 96
x = 32
Therefore, the measures of the three angles are:
Angle A = Angle B = x = 32 degrees
Angle C = x + 84 = 32 + 84 = 116 degrees