Maths - Geometry
1. In the following figure, the value of x is 
- Option : B
- Explanation : ∠CBA =180° -65°=115°.
∠DCB =180° -80°=100°.
∠EDC=1I5°.
∠A =90°.
∠DEA =540°.
- (115°+ 100° + 115° + 90°) =120°.
[sum of all angles 'in a pentagon is
540°].
∠x = 180° -120°=60°
- Option : D
- Explanation : As, we know that
∠AOC+ ∠BOC = 180° (Linear Pair)
⇒ 50° + ∠BOC = 180°
⇒ ∠BOC = 180° - 50°
= 130°
- Option : A
- Explanation : As, ∠ACB = 180° - (∠ABC+ ∠BAC)
= 180° - (50°+ 30°) = 100° (Sum of angles of a triangle)
∴ ∠ACD = 180° - 100° = 80° (Linear Pair)
∴ ∠AED = ∠ACD + ∠EDC
= 80° + 25° = 105° (Exterior Angle Theorem).
4. The sum oflength oftwo sides of a triangle is always
- Option : B
- Explanation : Sum of length of two sides of a triangle is always greater than the third side.
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