Observe the given figure.
Since, it is given that the angles ACD is supplementary to angles ACE and BCD. Angle ACD is congruent to angle BCE.
We have to identify the correct statements.
1. Consider the first statement
"Angle ACE is supplementary to angle BCD". Since, they are not adjacent angles. Therefore, it does'not form supplementary angles. So, this is not the correct statement.
2. Consider the second statement
"Angle BCE is supplementary to angle ACE".Since, they are adjacent angles. Therefore, it form linear pair. So, they are supplementary angles. So, this is the correct answer.
3. Consider the third statement
"Angle BCD is supplementary to angle BCE". Since, they are adjacent angles. Therefore, it form linear pair. So, they are supplementary angles. So, this is the correct answer.
4. Consider the fourth statement
"Angle ACE is congruent to angle BCE". Since, these angles are adjacent angles. They are not vertically opposite angles. Hence, they are not congruent.
5. Consider the fifth statement
"Angle BCD is congruent to angle ACE".Since, these angles are not adjacent angles. As we can observe that hey are vertically opposite angles. Hence, they are congruent.
