Question

Since AOB forms a line segment, /XOB and /AOX are supplementary by the ____. Using the definition of

supplementary angles, m/XOB + m/AOX = 180°. Since it is given that /XOB = /AOX, then m/XOB = m/AOX. Applying the ____, then 2m/XOB = 180° After dividing, m/XOB = 90°

Answer 1

Given that AOB forms a line segment we can conclude that ∠XOB and ∠AOX are supplementary angles. By the definition of supplementary angles we know that the sum of their measures is 180°.

Therefore we can write the equation:

∠XOB + ∠AOX = 180°

Since it is given that ∠XOB = ∠AOX we can substitute ∠AOX with ∠XOB in the equation:

∠XOB + ∠XOB = 180°

Combining like terms we have:

2∠XOB = 180°

Now we want to solve for the measure of ∠XOB. To isolate ∠XOB we can divide both sides of the equation by 2:

(2∠XOB)/2 = 180°/2

Simplifying we get:

∠XOB = 90°

Therefore the measure of angle ∠XOB is 90°.