Answer: Second choice: <span>It is possible for an obtuse angle to have both a complement and a supplement. </span> Explanation: Let's examine the given choices:
First choice: <span>It is possible for angles to be both vertical and complementary. Vertical angles are equal angles. Complementary angles means that the two angles add up to 90 degrees. Two angles can be both vertical and complementary if the measure of each is 45. By this, the two angles are equal and their summation is 90 degrees. Therefore, this statement is correct
Second choice: </span><span>It is possible for an obtuse angle to have both a complement and a supplement. </span>Complement angles means that their sum is 90 degrees. Supplement angles means that their sum is 180 degrees. Since the measure of an obtuse angle is greater than 90, therefore, it cannot have a complement. Therefore, this statement is not correct
Third choice: <span>It is possible for an acute angle to have both a complement and a supplement. </span>Complement angles means that their sum is 90 degrees. Supplement angles means that their sum is 180 degrees. Since the measure of an acute angle is less than 90, therefore, it can have both a complement and a supplement. Therefore, this statement is correct
Fourth choice: <span>It is possible for angles to be both congruent and supplementary </span>Congruent angles means that they are equal Supplement angles means that they add up to 180 degrees. Two angles can be both congruent and supplement if the measure of each is 90. By this, the two angles are equal and their summation is 180 degrees. Therefore, this statement is correct
Based on the above, the only incorrect statement is the second choice.
