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steposvetlana [31]
3 years ago
10

*URGENT* I don’t understand this and i don’t know the answers, please help!!

Mathematics
1 answer:
motikmotik3 years ago
8 0

Answer:

A) x>8

B) x<4

Step-by-step explanation:

A) 3x+5>29

3x>24

x>8 (It's greater than because the angle opposite is greater than the other angle)

B) 6x-17<7

6x<24

x<4 (It's less than because the angle opposite is smaller than the other angle)

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<u>Let's consider the facts at hand</u>:

  • By Vertical Angle Theorem ⇒ ∠BCE = ∠DCF
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  • Sides BE = DF

<u>Based on the diagram, triangles BCE and triangles DCF are similar</u>

   ⇒ based on the Angle-Angle theorem

      ⇒ since ∠BCE = ∠DCF and ∠BEC = ∠DFC

         ⇒ the two triangles are similar

Hope that helps!

<em>Definitions of Theorem I used:</em>

  • <u><em>Vertical Angle Theorem: </em></u><em>opposite angles of two intersecting lines must be equal</em>
  • <u><em>Angle-Angle Theorem:</em></u><em> if two angles of both triangles are equal, then the given triangles must be similar</em>

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