Answer:
x = 22
y = 6
Step-by-step explanation:
GIVEN :-
- ∠ABE = (4y + 2)°
- ∠FBE = (3x - 2)°
- ∠FBD = (5x + 6)°
TO FIND :-
GENERAL CONCEPT TO BE USED IN THIS QUESTION :-
- Complementary angles :- Two angles are said to be complementary if sum of measure of both angles is equal to 90°.
- Linear Pair :- Two angles are said to be a linear pair if both the angles lie on a straight line & sum of both angles is equal to 180°.
SOLUTION :-
In the figure given in the question , ∠FBE & ∠FBD are linear pair.
⇒ (3x - 2)° + (5x + 6)° = 180°
⇒ 8x + 4 = 180
⇒ 8x = 176
⇒ x = 22°
Also , AB⊥CF.
⇒ ∠ABE & ∠FBE are complementary angles.
⇒ (4y + 2)° + (3x - 2)° = 90°
⇒ 4y + (3×22) = 90 [∵ Putting x = 23]
⇒ 4y + 66 = 90
⇒ 4y = 24
⇒ y = 6
