triangle upper T upper I upper C is an Isosceles triangle with a vertex angle I. If the measure of angle upper I equals 90 degrees, then find the measure of angle upper T.
(1 point)
Responses
15°
15°
45°
45°
90°
90°
30°
30°
Since triangle TIC is an isosceles triangle, angle TIC and angle C are congruent. If the measure of angle I is 90 degrees, then the sum of angle C and angle TIC must be 90 degrees as well.
Let's label angle TIC as angle T. Since angle TIC and angle C are congruent, angle C will also be labeled as angle T. Therefore, the measure of angle T is 90 degrees.
So the correct answer is 90°.
To find the measure of angle T in an isosceles triangle with a vertex angle I measuring 90 degrees, we need to apply the properties of isosceles triangles.
First, let's understand what an isosceles triangle is. An isosceles triangle is a triangle that has two equal sides (called the legs) and two equal angles opposite those sides.
In our given triangle, we are told that angle I measures 90 degrees. Since we know that the sum of angles in a triangle is 180 degrees, we can deduce the following:
Angle T + Angle T + Angle I = 180 degrees
Since angle I is given as 90 degrees, we can substitute this value into the equation:
Angle T + Angle T + 90 degrees = 180 degrees
Simplifying the equation further, we have:
2 * Angle T + 90 degrees = 180 degrees
Subtracting 90 degrees from both sides of the equation, we get:
2 * Angle T = 90 degrees
Dividing both sides of the equation by 2, we find:
Angle T = 45 degrees
So, the measure of angle T in the given isosceles triangle is 45 degrees.
Therefore, the correct answer is 45°.