Part A: Exterior angle is 110^(∘), and remote interior angles are 35^(∘)+75^(∘) = 110^(∘).
Part B: Exterior angle is 140^(∘), and remote interior angles are 70^(∘)+70^(∘) = 140^(∘).
Part C: Exterior angle is 148^(∘), and remote interior angles are 48^(∘)+148^(∘) = 148^(∘).
Part D: Exterior angle is 108^(∘), and remote interior angles are 36^(∘)+72^(∘) = 108^(∘).
We see a pattern of the exterior angle of a triangle — its remote interior angles are identical.
b As we mentioned in Part A, the sum of the remote interior angles should equal the exterior angle. Let's identify these in the diagram.
With this information we can write the following equation.
m∠ x=m∠ a+m∠ b
c In the diagram we notice that ∠ x and ∠ c form a linear pair, which means they are supplementary. Additionally, according to the Triangle Angle Sum Theorem the three angles of the triangle, ∠ a, ∠ b, and ∠ c sum to 180^(∘)
Since both the linear pair and the interior angles of the triangle equal 180^(∘), we can equate them.
m∠ a+m∠ b+m∠ c = 180^(∘)
m∠ x+m∠ c = 180^(∘)
⇓
m∠ a+m∠ b+m∠ c= m∠ x+m∠ c
Let's simplify the equation.
