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

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) °