Question

If m□ebd=4x-8 and m□ebc=5x+20,find the value of x and m□ebc

Answer 1

m□ebd=4 x-8 and m□ebc=5 x+20

This is solvable only if e b is the initial side and b d and b c lies on opposite side of each other and lies on a line i.e c,b,d are Collinear.

∠ebd and ∠ebc will form a linear pair.The meaning of linear pair is that angles forming on one side of a straight line through a common vertex which are adjacent is 180°.

i.e

∠ ebd + ∠ebc = 180°

4 x- 8 + 5x + 20= 180°

adding like terms

⇒ 9 x +12 =180°

⇒ 9 x = 180° - 12

⇒ 9 x = 168°

⇒ x =( 168/9)°=(56/3)°

now  m□ebc =5 x +20

       = 5 × 56/3 + 20

       = 280/3 + 20

      =340/3

m□ebc=( 340/3)°

So, solution set is x =(56/3)° and  m□ebc =(340/3)°