Find : x + y+ z + w

Answers
hope this helps you....

Answer:
<x = 125°
Step-by-step explanation:
Given,
<BEF = 60°
<CDG = 50°
< BAC = 40°
<ABE = <ACD = <x
To Find:
<x
Solution:
<BEF + <BED = 180° (Straight Line)
=> 60° + <BED = 180°
=> <BED = 180° - 60°
=> <BED = 120°
<CDE + <CDG = 180° (Straight Line)
=> <CDE + 50° = 180°
=> <CDE = 180° - 50°
=> <CDE = 130°
Sum of all angles of a polygon is given by formula → 180° (n - 2)
Where, n = Number of sides of the polygon.
Here,
Polygon ABEDC has 5 sides.
So, n = 5
Therefore,
Sum of all angles of a polygon = 180° (n - 2)
Sum of all angles of ABEDC = 180° (5 - 2)
Sum of all angles of ABEDC = 180° X 3
Sum of all angles of ABEDC = 540°
< BAC + <ACD + <CDE + <BED + <ABE = 540°
=> 40° + <ACD + 130° + 120° + <ABE = 540°
=> 290° + <ACD + <ABE = 540°
290° + 2<ACD = 540°
=> 2<x = 540° - 290°
=> 2<x = 250°
=> <x = 250°/2
=> <x = 125°
Hope it helps you.
Thanks :)
