5. 015) Find the value of x in the given figure: -
Attachments:

Answers
Answered by
6
⠀⠀⠀⠀⠀⠀⠀
Given
⠀⠀⠀⠀⠀⠀⠀
- EG = FG
⠀⠀⠀⠀⠀⠀⠀
- ∠FGH = 105°
⠀⠀⠀⠀⠀⠀⠀
To Find
⠀⠀⠀⠀⠀⠀⠀
- Value of x
⠀⠀⠀⠀⠀⠀⠀
We know
⠀⠀⠀⠀⠀⠀⠀
Angles opposite to the equal sides are also equal. So, ∠GEF = ∠EFG
⠀⠀⠀⠀⠀⠀⠀
Solution
⠀⠀⠀⠀⠀⠀⠀
➨∠EGF + ∠FGH = 180° [ Linear Pair ]
➨ x + 105° = 180°
➨ x = 180 - 105
➨ x = 75°
⠀⠀⠀⠀⠀⠀⠀
∠EGF = 75°
⠀⠀⠀⠀⠀⠀⠀
∠GEF = ∠EFG = x
⠀⠀⠀⠀⠀⠀⠀
➨∠GEF + ∠EFG + ∠EGF = 180° [ Angle Sum Property of triangle ]
⠀⠀⠀⠀⠀⠀⠀
➨ x + x + 75° = 180°
⠀⠀⠀⠀⠀⠀⠀
➨ 2x + 75 = 180
⠀⠀⠀⠀⠀⠀⠀
➨ 2x = 180 - 75
⠀⠀⠀⠀⠀⠀⠀
➨ 2x = 105
⠀⠀⠀⠀⠀⠀⠀
➨ x = 52.5
⠀⠀⠀⠀⠀⠀⠀
Therefore, value of x = 52.5°
Similar questions