# In figure 2.6, li

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°

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