Question

In the figure below, ∠ f = 126˚ and ∠h = 104˚. Find the sum of ∠a , ∠b, ∠c and ∠d.

Answer 1

Hey bro!! here is your answer:
Final Result: 230°

Here, a,b ,c,d,e,f,g h represents respective angles.

We know that,
f + h = 126°+104°=230°

In Quad. EFGH,
e + f + g +h = 360° (Angle sum property of Quadrilateral EFGH. )

=>e+g+230°=360°
=>e+g= 130° --------(1)

Now,

In Triangle ABG,
a + b + g = 180° ( Angle sum property of triangle) --------(2)

In Triangle CDE,
c + d + e =180° (Same as above) ------(3)

Now,
Adding eq.(2) and (3),
a + b + c + d + e + g = 180°+180°
=> a + b+ c +d + 130° = 360° ( using eq. (1))
=> a + b + c + d = 360°-130°
=> a+ b + c + d = 230°

Hope, you understand my answer and it may helps you !!!

Answer 2

Hey bro !!

Here is your answer...

▶Given :- angle f = 126°
angle h = 104

▶To Find :- a + b + c + d = ?

▶Solution :-
f + h = 126 + 104
f + h = 230°

As we know sum of all angles of ◻efgh are 360°
So, e + f + h + g = 360
e + g = 360 - ( f + h )
e + g = 360 - 230
e + g = 130°. ............... (1)

In ∆gba,
sum of all angles are supplementary.
g + b + a = 180°. .............(2)

In ∆edc,
e + d + c = 180°. ......... (3)

Now add eq. (2) and eq. (3)

g + b + a + e + d + c = 180 + 180
a + b + c + d + e + g = 360
a + b + c + d = 360 - ( e + g )
a + b + c + d = 360 - 130. .. { from eq. (1) }
a + b + c + d = 230°

⏩sum of angle a, angle b angle c and angle is 230°

HOPE IT HELPS YOU....

THANKS
^-^