WISKUNDE
GRAAD 10
NOG OEFENINGE
Lyne en hoeke : antwoorde.
MATHEMATICS
GRADE 10
MORE EXERCISES
Lines and angles : answers.
Ant. / Ans. 1.4
3a + 5a + 2a = 180°
10a = 180°
a = 18°
Hoek / Angle 2a = 2 x 18° = 36°
Hoek / Angle 3a = 3 x 18° = 54°
Hoek / Angle 5a = 5 x 18° = 90°
Vr. / Qu. 1.4
Ant. / Ans. 1.8
3a − 50° = 2a + 30°
3a − 2a = 30° + 50°
a = 80°
Hoek / Angle 2a + 30° = 2 x 80° + 30° = 190°
Hoek / Angle 3a − 50° = 3 x 80° − 50° = 190°
Vr. / Qu. 1.8
Antwoord / Answer 2
2.1 ∠F
2 + ∠F
3 = 180°
. . . EFGH a rt.lyn / EFGH a straight line
50° + ∠F
3 = 180°
. . . gegee / given
∠F
3 = 130°
2.2 ∠G
2 = ∠F
2 . . . ooreenk. ∠'e, AB || CD / corresp. ∠'s, AB || CD
= 50°
2.3 ∠F
4 = ∠F
2 . . . regoorst. ∠'e / vert. opp, ∠'s
= 50°
2.4 ∠G
3 = ∠F
3 . . . ooreenk. ∠'e, AB || CD / corresp. ∠'s, AB || CD
= 130°
2.5 ∠G
4 = ∠G
2 . . . regoorst. ∠'e / vert. opp, ∠'s
= 50°
OF / OR
∠G
4 = ∠F
4 . . . ooreenk. ∠'e, AB || CD / corresp. ∠'s, AB || CD
= 50°
Antwoord / Answer 3
3.1 ∠1 + ∠2 = 180°
. . . rt.lyn / straight line
38° + ∠2 = 180°
. . . gegee / given
∠2 = 142°
3.2 ∠3 = ∠1
. . . regoorst. ∠'e / vert. opp. ∠'s
= 38°
3.3 ∠5 = ∠1
. . . ooreenkst. ∠'e, PQ || RS / corresp. ∠'s, PQ || RS
= 38°
3.4 ∠8 = ∠2
. . . verwis. ∠'e, AB || CD / alt. ∠'s, AB || CD
= 142°
3.5 ∠6 = ∠2
. . . ooreenkst. ∠'e, PQ || RS / corresp. ∠'s, PQ || RS
= 142°
OF / OR
∠6 = ∠8
. . . regoorst. ∠'e / vert. opp. ∠'s
= 142°
Antwoord / Answer 4
4.1 ∠D
1 + ∠D
2 = 180°
. . . rt.lyn / straight line
72° + ∠D
2 = 180°
. . . gegee / given
∠D
2 = 108°
∠B
3 = ∠D
2 . . . ooreenk ∠'e, AB || CD / corresp. ∠'s AB || CD
= 108°
4.2 ∠B
1 + ∠B
2 = ∠D
1 . . . ooreenk ∠'e, AB || CD / corresp. ∠'s, AB || CD
∠B1 + 21° = 72° . . . gegee / given
∠B1 = 51°
4.3 ∠C = ∠B2 . . . verwis. ∠'e, AB || CD / alt. ∠'s, AB || CD
= 21°
Antwoord / Answer 5
∠DAB + ∠BAC + ∠EAC = 180°
. . . rt. lyn / str. line
∠DAB = ∠B
. . . verwis. ∠'e, DAE || BC / alt. ∠'e, DAE || BC
∠EAC = ∠C
. . . verwis. ∠'e, DAE || BC / alt. ∠'e, DAE || BC
∴ ∠BAC + ∠B + ∠C = 180°
Antwoord / Answer 6
∠ECD = ∠B
. . . ooreenk. ∠'e, AB || EC / corresp.. ∠'e, AB || EC
∠ACE = ∠A
. . . verwis. ∠'e, AB || EC / alt. ∠'e, AB || EC
∠ECD + ∠ACE = ∠B + ∠A
∴ ∠ACD = ∠A + ∠B