Question

SHORT ANSWER TYPE QUESTIONS Q5. Determine the value of x in the given figure if ABIICDIIEF i. ii. А. B A B 130° 65 E 25° 120° D C​

Answer 1

Answer:

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As per the diagram, lines CD∣∣EF and CE is transveral.

We know that sum of interior angles is equal to 180

∠ECD+∠CEF=180

∠ECD+130o=180o

∠ECD=180−130

∠ECD=50o

As per the diagram, lines AB∣∣CD and CA is transveral.

We know that alternate angles are equal.

∠BAC=∠ACD 

∠BAC=∠ACE+∠ECD

70o=∠ACE+50

20o=∠ACE

∴∠ACE=20

Answer 2

If DE∣∣AB, then ΔCDE∼ΔABC

By property of similar triangles:

ACCD=BCCE

⟹4x+22x+3=4x+4x

Cross-multiplying:

(x+3)(4x+4)=x(4x+22)

⟹4x2+16x+12=4x2+22x

12=6x⟹x=2