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 l_{1} and l_{2} 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 l_{1} and l_{2} 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 l_{1} and l_{2} 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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