Answer:
Explanation:
To prove that <2 = 23, we can use the paragraph method with the given information:
1. Given: 21 and 22 form a linear pair.
Reason: A linear pair is formed when two adjacent angles add up to 180°.
2. Given: m/1 + <3 = 180°
Reason: The sum of angle measures in a linear pair is 180°.
3. Let's assume that <2 = x (where x is the measure of angle 2).
Reason: This is our initial assumption to start the proof.
4. Since 21 and 22 form a linear pair, we know that the measure of angle 21 + the measure of angle 22 = 180°.
Reason: This is based on the definition of a linear pair.
5. From statement 3, we assumed that <2 = x. Therefore, the measure of angle 21 + x = 180°.
Reason: We substitute the value of <2 from our assumption into the equation.
6. We can subtract the measure of angle 21 from both sides of the equation to isolate x: x = 180° - measure of angle 21.
Reason: This step helps us find the measure of <2.
7. Given: 21 and 22 form a linear pair. Since angle 21 is adjacent to angle 22, their measures add up to 180°.
Reason: This is a restatement of the information given in statement 1.
8. By substitution, we can replace the measure of angle 21 with 180° - measure of angle 22 in statement 6: x = 180° - (180° - measure of angle 22).
Reason: We substitute the measure of angle 21 from statement 7 into the equation.
9. Simplifying the expression in statement 8, we get: x = measure of angle 22.
Reason: The subtraction of 180° - 180° cancels out, leaving us with the measure of angle 22.
10. Therefore, we have proven that <2 = 23, as we initially assumed that x (the measure of angle 2) is equal to 23.
Reason: By substituting the measure of angle 22 into our initial assumption, we find that x is indeed equal to 23.
In conclusion, using the paragraph method and the given information, we have proven that <2 = 23.