In figure 2.6, line p|| line q and line and line m are transversals. Measures of some angles are shown. Hence find the measures of ∠ a, ∠ b, ∠ c∠ d.

Given line P ∥ line Q and line L and M are transversal.

To find: ∠ a, ∠ b, ∠ c∠ d.

Construction: extend G and E in answer diagram.

∠ a + ∠ e = 180° (linear pair angle) means that linear pair is a pair of adjacent, supplementary angle.

Adjacent means next to each other, and supplementary means that measures of the two angles add up to equal 180°.

∠ a + 110° = 180° (given)

∠ a = 180° -110°

∠ a = 70°

∠ a ≅ ∠ g (vertically opposite angles formed are congruent

∠ a = 70° (prove above)

∠ 70° ≅ ∠ g

Line P || line Q and line L transversals (given)

∠ g = ∠ b (corresponding angles)

∠ b = 70°

Line P || line Q and line M is transversal (given)

∠ c ≅ ∠ f (corresponding angles) if two parallel line are cut by a transversal, then the pairs of corresponding angle are congruent.

So, ∠ f = 115° (given)

Then, ∠ c = 115°

∠ d + ∠ f = 180° (linear pair angle)

∠ d + 115° = 180° (given)

∠ d = 180° -115°

∠ d = 65°