Question 99 In the given figure AE GF BD - AB CG DF and - CHE -120- Find - ABC and - CDE-

The correct option is Since, BD || AE and CG is transversal. Therefore,∠ BCH = ∠ EHC ⇒∠ BCH = 120^∘ Again CG ||DF and BD is transversal. Therefore,∠ BCH ...

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Standard VII

Mathematics

Transversal

Question 99 I...

Question

Question 99

In the given figure $A E | | G F | | B D, A B | | C G | | D F$ and $∠ C H E = 120^{\circ}$ , Find $∠ A B C$ and $∠ C D E .$

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Solution

Since, $B D | | A E a n d C G$ is transversal.
Therefore, $∠ B C H = ∠ E H C \Rightarrow ∠ B C H = 120^{\circ}$
Again CG ||DF and BD is transversal.
Therefore, $∠ B C H = ∠ C D E \Rightarrow ∠ C D E = 120^{\circ}$
Also, $A B | | C G a n d B C$ is transversal.
Therefore $∠ A B C + ∠ B C H = 180^{\circ} \Rightarrow ∠ A B C = 180^{\circ} - 120^{\circ} \Rightarrow ∠ A B C = 60^{\circ}$

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Question 99 In the given figure AE||GF||BD,AB||CG||DF and ∠CHE=120∘, Find ∠ABCand ∠CDE.

Since, BD||AE and CG is transversal. Therefore,∠BCH=∠EHC⇒∠BCH=120∘ Again CG ||DF and BD is transversal. Therefore,∠BCH=∠CDE⇒∠CDE=120∘ Also, AB||CG and BC is transversal. Therefore∠ABC+∠BCH=180∘⇒∠ABC=180∘−120∘⇒∠ABC=60∘

Question 99

In the given figure $A E | | G F | | B D, A B | | C G | | D F$ and $∠ C H E = 120^{\circ}$ , Find $∠ A B C$ and $∠ C D E .$