Question

18. In Fig. 11.47, for which value of x is l¹ || 1²?
please give answer in step-by-step explaination​

Answer 1

[NOTE -: I have labelled some lines in addition for better understanding. Refer the attachement.]

Given

• l₁ ║ l₂
• ∠DBA = 78°
• ∠CAG = 35°
• ∠BCA = 90°

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To Find

• The value of x°

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Solution

Since l₁ = l₂, the line BA is the transversal.

So we can see that,

→ ∠DBA = ∠BAG = 78° [Alternate Angles]

⇒ ∠BAG = ∠BAC + ∠CAG

⇒ 78° = ∠BAC + 35°

⇒ ∠BAC = 78° - 35°

⇒ ∠BAC = 43°

∴ ∠BAC = 43°

⇒ ∠ABC + ∠BCA + ∠BAC = 180°  [Sum of Interior Angles of Traingle Proeprty]

⇒ x + 90° + 43° = 180°

⇒ x + 133° = 180°

⇒ x = 180° - 133°

⇒ x = 47°

∴ The value of 'x' is 47°

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Answer 2

kindly see the attachment for your answer