triangle TIC is an isosceles triangle with vertex angle I. Find the measures of the base angles of triangle TIC if m<I = 100 degrees
Since triangle TIC is isosceles, the base angles are congruent. Let's denote the base angles as angle T and angle C.
The sum of the angles in a triangle is 180 degrees. Since angle I is 100 degrees, the sum of angles TCI and TIC is 180 - 100 = 80 degrees.
Since angles TCI and TIC are congruent, we can divide 80 by 2 to find the measure of each of these angles: 80 / 2 = 40 degrees.
Therefore, the measure of each of the base angles of triangle TIC is 40 degrees.
80 degrees
50 degrees
60 degrees
40 degrees
I apologize for the confusion in my previous response.
Let's denote the base angles of triangle TIC as angle T and angle C.
Since triangle TIC is isosceles, the base angles are congruent. Thus, the measure of angle T = the measure of angle C.
The sum of the angles in a triangle is 180 degrees. We know that angle I = 100 degrees. Using the fact that the sum of the angles in a triangle is 180 degrees, we can find the measure of angle T and angle C.
angle T + angle C + angle I = 180 degrees
angle T + angle T + angle I = 180 degrees (substituting angle T for angle C)
2(angle T) + 100 = 180
2(angle T) = 180 - 100
2(angle T) = 80
angle T = 80 / 2
angle T = 40 degrees
Since angle T = 40 degrees, angle C is also 40 degrees.
Therefore, the measures of the base angles of triangle TIC are both 40 degrees.