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# Justifying Angle Relationships

A transversal is a line that intersects two strains in the identical aircraft at two completely different factors. Transversal and the 2 strains type eight angles.

On this part, you’ll learn to justify the relationships between the eight angles. Corresponding Angles :

Angles lie on the identical facet of the transversal t, on the identical facet of strains a and b.

Instance : ∠ 1 and ∠ 5

Alternate Inside Angles :

Angles are nonadjacent angles that lie on reverse sides of the transversal t, between strains a and b.

Instance : ∠ 3 and ∠ 6

Alternate Exterior Angles :

Angles lie on reverse sides of the transversal t, exterior strains a and b.

Instance : ∠ 1 and ∠ 8

Identical-Facet Inside Angles :

Angles lie on the identical facet of the transversal t, between strains a and b.

Instance : ∠ 3 and ∠ 5

## Solved Issues

Drawback 1 :

A transversal cuts the 2 parallel strains and varieties eight angles.  Describe the relationships between the angles within the diagram given under. Resolution :

Corresponding Angles :

∠CGE and ∠AHG, ∠DGE and ∠BHG, ∠CGH and ∠AHF, ∠DGH and ∠BHF ; congruent.

Alternate Inside Angles :

∠CGH and ∠BHG, ∠DGH and ∠AHG ; congruent.

Alternate Exterior Angles :

∠CGE and ∠BHF, ∠DGE and ∠AHF ; congruent.

Identical-Facet Inside Angles :

∠CGH and ∠AHG, ∠DGH and ∠BHG ; supplementary.

Drawback 2 :

Within the determine given under,  let the strains l1 and l2 be parallel and m is transversal. If F = 65°, utilizing the angle relationships,  discover the measure of every of the remaining angles. Resolution :

From the given determine,

F and H are vertically reverse angles and they’re equal.

Then, H  =  F ——-> H  =  65°

H and D are corresponding angles and they’re equal.

Then, D  =  H ——-> D  =  65°

D and B are vertically reverse angles and they’re equal.

Then, B  =  D ——-> B  =  65°

F and E are collectively type a straight angle.

Then, we’ve

F + E  =  180°

Plug F  =  65°

F + E  =  180°

65° + E  =  180°

E  =  115°

E and G are vertically reverse angles and they’re equal.

Then, G  =  E ——-> G  =  115°

G and C are corresponding angles and they’re equal.

Then, C  =  G ——-> C  =  115°

C and A are vertically reverse angles and they’re equal.

Then, A  =  C ——-> A  =  115°

Due to this fact,

A  =  C  =  E  =  G  =  115°

B  =  D  =  F  =  H  =  65°

Drawback 3 :

Within the determine given under,  let the strains l1 and l2 be parallel and t is transversal. Utilizing angle relationships, discover the worth of x. Resolution :

From the given determine,

(2x + 20)° and (3x – 10)° are corresponding angles.

So, they’re equal.

Then, we’ve

(2x + 20)°  =  (3x – 10)°

2x + 20  =  3x – 10

30  =  x

Drawback 4 :

Within the determine given under,  let the strains l1 and l2 be parallel and t is transversal. Utilizing angle relationships, discover the worth of x. Resolution :

From the given determine,

(3x + 20)° and 2x° are consecutive inside angles.

So, they’re supplementary.

Then, we’ve

(3x + 20)° + 2x°  =  180°

3x + 20 + 2x  =  180

5x + 20  =  180

5x  =  160

x  =  32

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