The conjecture that must be true is statement B, because sum of two supplementary angles = 180 degrees.
If both angles are congruent, it means they are equal. Therefore, each will be 90 degrees which is a right angle. (Option B)
Statement A: NOT TRUE
Sum of two angles that are supplementary = 180 degrees
Two adjacent angles on a straight line can only be supplementary.
However, if the two adjacent angles are not on a straight line, they wont be supplementary.
Statement B: TRUE
Supplementary angles added together = 180 degrees.
If both angles are congruent, it means they are equal. Therefore, each will be 90 degrees which is a right angle.
Statement C: NOT TRUE
Two congruent angles may share a common vertex, but may not be vertically opposite each other.
Two congruent angles on a straight line are linear pair angles, not vertical angles.
Statement D: NOT TRUE
Acute angles are less than 90 degrees. E.g. 70 and 80 degrees are acute angles.
Their sum, 70 + 80 is greater than 90°.
Therefore, the conjecture that must be true is statement B, because sum of two supplementary angles = 180 degrees.
If both angles are congruent, it means they are equal.
Therefore, each will be 90 degrees which is a right angle. (Option B)
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