Question

Solve for x. Show all your work

Answer 1

42°

Step-by-step explanation:

$\angle BAE =180\degree -132\degree$

(Angles in linear pair)

$\angle BAE =48\degree$

$\angle AEB =90\degree..(\because \overrightarrow{EC}\perp\overrightarrow{ED})$

$\angle ABE = 180\degree-(48\degree+90\degree)$

(Angle sum postulate of a triangle)

$\implies\angle ABE = 180\degree-138\degree$

$\implies\angle ABE = 42\degree$

$\angle CDE =\angle ABE = 42\degree$

(corresponding angles)

$\implies x\degree=\angle CDE$

(vertical angles)

$\implies x\degree=42\degree$

$\implies x=42$