Question

86. For a triangle with two angles measuring 45°, which of the following must be false?

O A) It is a right triangle.
O B) Two legs of the triangle are equal in length.
O C) The hypotenuse of the triangle is longer than its two sides.
O D) All three angles in the triangle are acute.

Answer 1

A triangle with two angles measuring 45° cannot be a right triangle, isosceles, or have all three angles acute.

Step-by-step explanation:

For a triangle with two angles measuring 45°, the following statements must be false:

1. A) It is a right triangle: A right triangle has one angle measuring 90°, so if two angles are 45°, it cannot be a right triangle.
2. B) Two legs of the triangle are equal in length: In an isosceles right triangle, two legs are equal in length, but if two angles are 45°, the triangle may not be isosceles.
3. C) The hypotenuse of the triangle is longer than its two sides: In a right triangle, the hypotenuse is always longer than the other two sides, but since it is not a right triangle, this statement may not be true.

Therefore, the false statement is D) All three angles in the triangle are acute, as the sum of the angles in a triangle is always 180°, and with two angles measuring 45°, the third angle must be greater than 90° to satisfy this property.

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