Question

Solve for x. Show all your work

Answer 1

42°

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`