It is given that ΔABC ΔDFE. If ∠A = 30°, ∠C = 50°, AB = 5 cm, AC = 8 cm and DF = 7.5 cm, then which of the following is true? 1. DE = 12 cm, ∠F = 50° 2. DE = 12 cm, ∠F = 100° 3. EF = 12 cm, ∠D = 100° 4. EF = 12 cm, ∠D = 30°

Question

KnowledgeBoat · Accepted Answer

Given, ∠A = 30° ∠C = 50° In triangle ABC, ∠A + ∠B + ∠C = 180° ∠B = 180° - (∠A + ∠C) ∠B = 180° - (30° + 50°) ∠B = 180° - 80° ∠B = 100°. As the triangles are similar, the corresponding angles will be equal. So, ∠F = ∠B = 100° Since the triangles are similar, the ratio of corresponding sides is proportional, DE = 12 cm, ∠F = 100° Hence, option 2 is the correct option.

Mathematics

It is given that ΔABC ∼ ΔDFE. If ∠A = 30°, ∠C = 50°, AB = 5 cm, AC = 8 cm and DF = 7.5 cm, then which of the following is true?
DE = 12 cm, ∠F = 50°
DE = 12 cm, ∠F = 100°
EF = 12 cm, ∠D = 100°
EF = 12 cm, ∠D = 30°

Similarity

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In ΔABC, DE ∥ BC so that AD = (7x − 4) cm, AE = (5x − 2) cm, DB = (3x + 4) cm and EC = (3x) cm.
Then x equals:
2.5
3
4
5

Mathematics

It is given that ΔABC ∼ ΔDFE. If ∠A = 30°, ∠C = 50°, AB = 5 cm, AC = 8 cm and DF = 7.5 cm, then which of the following is true?DE = 12 cm, ∠F = 50°DE = 12 cm, ∠F = 100°EF = 12 cm, ∠D = 100°EF = 12 cm, ∠D = 30°

Similarity

Related Questions

In ΔABC, DE ∥ BC so that AD = (7x − 4) cm, AE = (5x − 2) cm, DB = (3x + 4) cm and EC = (3x) cm.Then x equals:2.5345

It is given that ΔABC ∼ ΔDFE. If ∠A = 30°, ∠C = 50°, AB = 5 cm, AC = 8 cm and DF = 7.5 cm, then which of the following is true?
DE = 12 cm, ∠F = 50°
DE = 12 cm, ∠F = 100°
EF = 12 cm, ∠D = 100°
EF = 12 cm, ∠D = 30°

In ΔABC, DE ∥ BC so that AD = (7x − 4) cm, AE = (5x − 2) cm, DB = (3x + 4) cm and EC = (3x) cm.
Then x equals:
2.5
3
4
5