Question

a. m∠abc - m∠bac = 10
b. m∠abc - m∠bac = 20
c. m∠abc - m∠bac = 30
d. m∠abc - m∠bac = 80

Explanation:

Step1: Find the interior - angle at D.

The angle adjacent to the 130° exterior - angle at D is an interior angle of the triangle. Let's call it $\angle BDC$. Since an exterior angle and its adjacent interior angle are supplementary, $\angle BDC=180 - 130=50^{\circ}$.

Step2: Use the angle - sum property of a triangle.

In $\triangle BCD$, we know that the sum of the interior angles of a triangle is 180°. Let $\angle BCD = x = 70^{\circ}$ and $\angle BDC = 50^{\circ}$. Let $\angle DBC=\angle 2$. Then $\angle 2=180-(70 + 50)=60^{\circ}$.
The exterior angle $\angle 1$ at B is supplementary to $\angle 2$. So $\angle 1 = 180-\angle 2=120^{\circ}$.
We want to find the relationship between $\angle 1$ and $\angle 2$. $\angle 1-\angle 2=120 - 60 = 60^{\circ}$.

Answer:

C. $m\angle 1 - m\angle 2=60$