Question

Write the proof in a paragraph format.Since forms a line segment, and are supplementary by the . Using the definition of supplementary angles, . Since it is given that , then . Applying the , then . After dividing, .

Answer 1

Given:

m∠XOB = 90 degrees

Where AOB forms a line segment.

The figure below represents this situation.

From the figure above, we can see that:

m∠XOB = m∠AOX

m∠XOB + m∠AOX = 90 + 90 = 180 degrees

The linear pair theorem states that if two angles form a linear pair, then they are supplementary angles and supplementary angles are angles that sum up to 180 degrees.

Hence, ∠XOB and ∠AOX are supplementary angles by applyng the linear pair theorem.

Also, by applying the substitution property of equality, 2(m∠XOB = 180 degrees).

ANSWER:

• Linear pair theorem

• Substitution property of equality.