## Textbook Answers – Angles in Parallel Lines

**Workout**

Question 1:

(a) x = 112°

(b) x = 75°

(c) x = 30° y = 150°

(d) x = 99° y = 99° z = 81°

(e) x = 106° y = 106°

(f) x = 123° y = 70°

Question 2:

(a) angle g (b) angle f (c) angle d

(d) angle c (e) angle c (f) angle f

(g) angle f (h) angle d (i) angle e

(j) angle e

Question 3:

(a) x = 125° as ∠EFC and ∠ACB are corresponding so are the same

(b) x = 57° as ∠BCF and ∠CFB are alternate so are the same

(c) x = 70° as ∠EFH and ∠CFG are vertically opposite so are the same

(d) x = 75° as ∠DCF and ∠CFG are co-interior so add to 180°

(e) x = 127° as ∠DCF and ∠CFG are co-interior so add to 180°, so ∠CFG = 127°

∠CFG = ∠EFH as they are vertically opposite so are equal.

(f) x = 47° ∠EFH and ∠EFC are in a straight line, so add to 180°, so ∠EFC=47°

∠EFC = ∠ACB as they are vertically opposite so are equal.

Question 4:

(a) x = 59° ∠HIE = ∠IEF as they are alternate angles so are equal.

(b) x = 125° ∠EIH = ∠GHD as they are corresponding angles so ∠GHD=55°

∠GHD and ∠GHK are in a straight line, so ∠GHK = 125°

(c) x = 79° ∠ABE = ∠BEF as they are alternate angles s0 ∠BEF = 41°

BEF is a triangle so the angles add to 180°

∠BFE = 79°

(d) x = 67° ∠DEB and ∠BEF are in a straight line so ∠BEF = 46°

Triangle EBF is isosceles so ∠EFB = 67°

∠EFB = ∠ FBC as they are alternate angles

(e) x = 55° ∠BCG = ∠CGH as they are alternate angles, ∠CGH=48°

AGH is a triangle so the angles add up to 180°

∠GAH = 55°

(f) x = 152° ∠ABD =∠BDE as they are alternate angles, ∠BDE = 76°

Triangle BDE is isosceles, so ∠BED = 28°

∠BED and ∠BEF are in a straight line, so add to 180°

**Apply**

Question 1: AB and CD are parallel as ∠BAC + ∠DCA = 180° so they are co-

interior angles.

Question 2:

x = 70° ∠DCE = 70° as triangle CDE is isosceles.

∠DCE =∠CEF as they are alternate angles

Question 3: x = 25°

Question 4: x = 57°

Question 5: x + y + z = 180° as they are on a straight line.

Considering alternate angles, the two angles inside the triangle

are x and z. So the three angles in the triangle are x, y and z.

Therefore the angles in the triangle add up to 180°