Exercise 128 Page 204

a In the diagram, ∠ b and 101^(∘) are corresponding angles.

Because the two lines cut by the transversal are parallel, they are congruent according to the Corresponding Angles Theorem.

m∠ b = 101^(∘) We will also be able to determine m∠ f and m∠ h because this angle forms a linear pair with ∠ b, which means they are supplementary. m∠ f+ 101^(∘) = 180^(∘) ⇔ m∠ f=79^(∘) m∠ h+ 101^(∘) = 180^(∘) ⇔ m∠ h=79^(∘) Finally, we will be able to identify m∠ g because it is a vertical angle to 101^(∘).

None of the remaining angles can be determined, since they do not form an angle pair with any of the known angles.

b Let's add m∠ p= 130^(∘) and highlight the remaining angles we want to determine. We will also highlight ∠ n, which is the corresponding angle to 130^(∘).

Because the two lines cut by the transversal are parallel, they are congruent according to the Corresponding Angles Theorem.

m∠ n=130^(∘) Now we can determine m∠ m because this angle forms a linear pair with ∠ n, which means they are supplementary. m∠ m+ 130^(∘) = 180^(∘) ⇔ m∠ m=50^(∘) Let's add ∠ m to the diagram.