Textbook Answers – Angles in Parallel Lines

July 31, 2016

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°