A, B & C lie on a straight line. D, C & E lie on a different straight line. Angle y = 119° and angle z = 53°. Work out x , explaining each stage of your working in the comment box. The diagram is not drawn accurately.

The value of x is 114°.

Step-by-step explanation:

Firstly, we have to find ∠DBC and ∠DCB. In order to find ∠DBC, you have to subtract y from 180° as ABC is a straight line :

y + ∠DBC = 180°

Let y = 119°,

119° + ∠DBC = 180°

∠DBC = 180° - 119°

∠DBC = 61°

Next, you have to find ∠DCB by subtracting z and ∠DBC from 180° as total angles in a triangle is 180° :

z + 61° + ∠DCB = 180°

Let z = 53°,

53° + 61° + ∠DCB = 180°

∠DCB = 180° - 53° - 61°

∠DCB = 66°

Lastly, in order to find x, you have to subtract 56° from 180°

x = 180° - 66°

x = 114°

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