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2 years ago

6.soruyu çözer misiniz lütfen? Bu arada sağdaki okun sonunda E yazıyor. 65 PUAN!!!

Mathematics

2 answers:

Scorpion4ik [409]2 years ago

4 0

Answer:

< BCD = 60°

Step-by-step explanation:

AB || DE = > <DEC = 180° - 130° = 50°

<EDC = 180° - 110° = 70°

< BCD = 180° - (50° + 70°)

= 180° - 120°

= 60°

gavmur [86]2 years ago

3 0

Answer:

60°

Step-by-step explanation:

Extend AB beyond B, extend the segment with point D beyond D so it intersects BC at point E, and extend CD beyond D so that it intersects the extension of AB at point F (see attachment).

Now, we have two triangles: ΔCBF and ΔCED. Because DE || BF, then the two triangles are similar from equal angles.

ABF is a line, so ∠ABF = 180. We also know that ∠ABF = ∠ABC + ∠CBF = 130 + ∠CBF = 180. Then ∠CBF = 50°. Because the two triangles are similar and ∠CBF corresponds with ∠CED, then ∠CED = ∠CBF = 50°.

DE is also a line, so it is 180°. From similar reasoning as above, ∠CDE = 180 - 110 = 70°.

Since CDE is a triangle, its angles add up to 180°, so:

∠CED + ∠ECD + ∠CDE = 180

50 + ∠ECD + 70 = 180

∠ECD = ∠BCD = 60°

The answer is 60°.

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