<1 and <2 are a linear pair. true or false
<3 and <5 are vertical angles. true or false
<3 and <4 are complementary angles. true or false
<4 and <5 are supplementary angles. true or false
The answer to the first statement is false. <1 and <2 are not a linear pair.
The answer to the second statement is false. <3 and <5 are not vertical angles.
The answer to the third statement is false. <3 and <4 are not complementary angles.
The answer to the fourth statement is true. <4 and <5 are supplementary angles.
To determine the true or false values for the given statements, let's understand the definitions of each type of angle pair:
1. Linear pair: Two angles are said to form a linear pair if their measures add up to 180 degrees and they share a common vertex and a common side.
2. Vertical angles: Two angles are said to be vertical angles if they are formed by the intersection of two lines. Vertical angles are congruent, meaning they have the same measure.
3. Complementary angles: Two angles are said to be complementary angles if their measures add up to 90 degrees.
4. Supplementary angles: Two angles are said to be supplementary angles if their measures add up to 180 degrees.
Now, let's determine the true or false values for each statement:
1. <1 and <2 are a linear pair.
Since a linear pair is defined as two angles that add up to 180 degrees, we need more information to determine if <1 and <2 are a linear pair. Given the information provided, the statement is indeterminate.
2. <3 and <5 are vertical angles.
Vertical angles are formed by the intersection of two lines, and they have equal measures. Without more information, it is not possible to determine if <3 and <5 are vertical angles. The statement is indeterminate.
3. <3 and <4 are complementary angles.
Complementary angles add up to 90 degrees. Without more information about the measures of <3 and <4, it is not possible to determine if they are complementary angles. The statement is indeterminate.
4. <4 and <5 are supplementary angles.
Supplementary angles add up to 180 degrees. Without more information, it is not possible to determine if <4 and <5 are supplementary angles. The statement is indeterminate.
Therefore, the true or false values for the given statements are indeterminate based on the information provided.