4. Which of the following is a converse of the statement?
A If two angles are congruent, then they are both 25 degrees.
B If two angles are not 25 degrees, then they are not congruent angles.
C None of the above.
D If two angles are not congruent angles, then they cannot both be 25 degrees.
If two angles are not congruent angles, then they cannot both be 25 degrees.
A None of the above.
B If two angles are not 25 degrees, then they are not congruent angles.
C If two angles are not congruent angles, then they cannot both be 25 degrees.
D If two angles are congruent, they are both 25 degrees.
6. Which of the following is a contrapositive of the statement?(2 points)
A If two angles are not congruent angles, then they cannot both be 25 degrees.
B If two angles are not 25 degrees, then they are not congruent angles.
C If two angles are congruent, they are both 25 degrees.
D None of the above.
.
A If two angles are not congruent angles, then they cannot both be 25 degrees.
The contrapositive of the statement "If two angles are congruent, then they are both 25 degrees" is:
B If two angles are not 25 degrees, then they are not congruent angles.
To determine the converse of a statement, we switch the hypothesis and the conclusion.
For the given statement, "If two angles are congruent, then they are both 25 degrees," the hypothesis is "two angles are congruent" and the conclusion is "they are both 25 degrees."
So, the converse of the statement is "If two angles are both 25 degrees, then they are congruent."
From the answer choices, option D states this converse: "If two angles are congruent, they are both 25 degrees." Therefore, the answer is option D.
Now let's move on to the contrapositive. To find the contrapositive of a statement, we switch and negate both the hypothesis and the conclusion.
For the given statement, "If two angles are congruent, then they are both 25 degrees," the negation of the hypothesis is "two angles are not congruent," and the negation of the conclusion is "they are not both 25 degrees."
So, the contrapositive of the statement is "If two angles are not congruent, then they are not both 25 degrees."
From the answer choices, option A states this contrapositive: "If two angles are not congruent angles, then they cannot both be 25 degrees." Therefore, the answer is option A.