Question

Write a justification for each step, given that BX bisects ∠ABC and m∠XBC = 45°.

1. BX bisects ∠ABC.
2. ∠ABX ∠XBC
3. m∠ABX = m∠XBC
4. m∠XBC = 45°
5. m∠ABX = 45°
6. m∠ABX + m∠XBC = m∠ABC
7. 45° + 45° = m∠ABC
8. 90° = m∠ABC
9. ∠ABC is a right angle.

Answer 1

The explanation of the statements can be given as

1. BX bisects ∠ABC. ( given in the question)

2. ∠ABX ∠XBC ( since triangle ABX and CBX are congruent, therefore, the angles are also congruent)

3. m∠ABX = m∠XBC ( Since both the angles are congruent therefore their measures will also be equal)

4. m∠XBC = 45° ( given)

5. m∠ABX = 45° ( since BX is bisecting, therefore, we. can say that ∠ABX will also be 45°)

6. m∠ABX + m∠XBC = m∠ABC ( property of dissection)

7. 45° + 45° = m∠ABC ( substituting the values)

8. 90° = m∠ABC ( addition of the value and getting the final answer)

9. ∠ABC is a right angle. ( since the final value is 90°, therefore, ∠ABC will be right angle)