Exercise 12 Page 540

We know that ∠ ABC and ∠ DBE are vertical angles. We also know that the measure of ∠ ABC is 40^(∘). We have to consider two cases. Let's graph each situation.

Case 1

In first situation, points A and D lies on different lines. We want to find the measure of ∠ ABD. Let's mark this angle.

We can see that the angles forms a straight line. This means that they are supplementary and the sum of their measures is 180^(∘).

m∠ ABD + 40^(∘) = 180^(∘)

SubEqn

LHS-40^(∘)=RHS-40^(∘)

m∠ ABD + 40^(∘) - 40^(∘) = 180^(∘) - 40^(∘)

SubTerms

Subtract terms

m∠ ABD = 140^(∘)

In this case, the measure of ∠ ABD is 140^(∘).

Case 2

Points A and D can also lie on the same line. We want to find the measure of ∠ ABD. Let's mark this angle.

We can see that the angle is a straight angle. This means that measure of ∠ ABD is 180^(∘).