90° . That's true of any triangle. Doesn't have to be isosceles.
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For an isosceles triangle with vertex 46 degrees, the sum of the remaining two base angles is 180-46 = 134 degrees. Base angles are equal because it's isosceles, so each angle is half of their sum. 134/2 = 67 degrees. Thus, any isosceles trapezoid formed inside that isosceles triangle by drawing parallel lines to the triangle's base, will have base angle measures of 67 degrees, which are triangle's base angles.
Depending how you halve it can be a right angle triangle or an isosceles trapezoid
Not true. A triangle with angles of 90, 45 and 45 is a right angled isosceles triangle. If you take a square piece of paper and fold it in half - from corner to corner - you will get this shape.
The triangle will then have 3 angles of 45, 45 and 90 degrees and take the shape of an isosceles right angle triangle.
An isosceles right triangle. Each of the acute angles is 45 degrees. The legs are equal, and each leg is sqrt(2) times half of the length of the hypotenuse.