ΔTIC is an isosceles triangle with vertex angle I. Find the measures of the base angles of ΔTIC if m∠I = 100º.

Question

(1 point)
Responses

80°

80°

50°

50°

60°

60°

40°

Answer 1

Since ΔTIC is an isosceles triangle, it has two equal base angles. Let's call these angles x.

The sum of the angles in a triangle is 180°. Therefore, we can write the equation:

∠I + ∠T + ∠C = 180°

Substituting the given values:

100° + x + x = 180°

Simplifying the equation:

100° + 2x = 180°

Subtracting 100° from both sides:

2x = 80°

Dividing both sides by 2:

x = 40°

So, the measure of each base angle (∠T and ∠C) is 40°.

Therefore, the correct answer is 40°.