If Two Angles Form A Linear Pair They Are - Since they form a linear pair, we have ∠xoz + ∠yoz = 180°. Therefore, we can set up the equation x + (x + 45) = 180. Subtracting we have, ∠dbc = ∠a + ∠c. ⇒ ∠xoz + ∠xoz = 180°. Web the linear pair perpendicular theorem states that if two angles of a linear pair are congruent, the lines are perpendicular. ⇒ ∠xoz = ∠yoz = 90°. Where ∠dbc is an exterior angle of ∠abc and, ∠a and ∠c are the remote interior angles. Here, ∠xoz and ∠yoz are congruent angles (m∠xoz = m∠yoz). Let us verify this with the following figure, as shown: Substituting the second equation into the first equation we get, ∠abc + ∠dbc = ∠a + ∠c + ∠abc.
Where ∠dbc is an exterior angle of ∠abc and, ∠a and ∠c are the remote interior angles. Here, ∠xoz and ∠yoz are congruent angles (m∠xoz = m∠yoz). Since the two angles form a linear pair, they must add up to 180 degrees. ⇒ ∠xoz + ∠xoz = 180°. Web the linear pair perpendicular theorem states that if two angles of a linear pair are congruent, the lines are perpendicular. Since they form a linear pair, we have ∠xoz + ∠yoz = 180°. Substituting the second equation into the first equation we get, ∠abc + ∠dbc = ∠a + ∠c + ∠abc. Solving for x gives us x = 67.5. Also, ∠abc and ∠dbc form a linear pair so, ∠abc + ∠dbc = 180°. Let us verify this with the following figure, as shown: Subtracting we have, ∠dbc = ∠a + ∠c. Therefore, we can set up the equation x + (x + 45) = 180. Web the linear pair theorem states that if two angles form a linear pair, then their measures add up to 180 degrees. ⇒ ∠xoz = ∠yoz = 90°. To understand this theorem, let’s first define what a linear pair is.