Which angles are corresponding remote angles to ∠ 3?
∠ 8, ∠ 9, and ∠ 10
Let's start by analyzing the given diagram. For the purposes of the solution, we will name the vertices of the triangles.
As we can see, ∠ 3 is an interior angle of △ ADC. Because ∠ 8 and ∠ 9 do not share a vertex or corner of the triangle with ∠ 3, they are the corresponding remote angles. Additionally, the sum of ∠ 2 and ∠ 3 is an interior angle of △ ABC.
Therefore, ∠ 9 and ∠ 10 are the corresponding remote angles of the sum of ∠ 2 and ∠ 3. Now, let's recall the Exterior Angle Inequality Theorem.
Exterior Angle Inequality Theorem
The measure of an exterior angle of a triangle is greater than the measure of either of its corresponding remote interior angles.
Considering this theorem, we can immediately say that ∠ 8 and ∠ 9 have greater measures than ∠ 3. Besides that we have another inequality involving ∠ 2, ∠ 3, and ∠ 10.
m∠ 10 > m∠ 2+ m∠ 3
⇓
m∠ 10 > m∠ 2 and m∠ 10 >m∠ 3
As a result, the measures of ∠ 8, ∠ 9, and ∠ 10 are greater than the measure of ∠ 3.
