Question

Compute the value of x

Answer 1

angle BAC = 180 - 120 = 60°

angle ACB = 180 - 112 = 68°

angle ABC = x = 180 - (68 + 60)

= 180 - 128

$\huge\boxed{x= 52°}$

Answer 2

Angles BAE and BAC are linear pairs.

∴ ∠BAC = 180° - ∠BAE = 180° - 120° = 60°

Also, angles DCA and BCA are linear pairs.

∴ ∠BCA = 180° - ∠DCE = 180° - 112° = 68°

The sum of angles in a triangle is 180°.

∠BAC + ∠ABC + ∠BCA = 180°

60° + 68° + x = 180°

128° + x = 180°

x = 180° - 128°

x = 52°