Question

Triangle TIC is an isosceles triangle with a vertex angle I. If the measure of Angle I = 90degrees, then find the measure of angle T.

A. 15degrees

B. 45degrees

C. 90degrees

D. 30degrees

Answer 1

It's B.  An isosceles triangle has two angles that are the same because they are across from 2 sides that are the same.  Therefore, these 2 angles must have the same measure.  Because of the triangle angle-sum theorem, all the angles add up to 180.  So 180-90 = 90 and 90/2 = 45

Answer 2

Applying the definition of an isosceles triangle, given that isosceles triangle TIC has a vertex angle I of 90 degrees, the measure of angle T is: B. 45degrees

Recall:

• An isosceles triangle has a vertex angle and two equal base angles.

Given that triangle TIC is an isosceles triangle:

• angle I is the vertex angle = 90 degrees
• angle T is a base angle
• angle C is also a base angle

Thus:

angle C and angle T are congruent or equal to each other.

• Therefore,

Angle T = (180 - 90)/2

Angle T = 90/2

Angle T = 45 degrees.

In summary, applying the definition of an isosceles triangle, given that isosceles triangle TIC has a vertex angle I of 90 degrees, the measure of angle T is: B. 45degrees

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