Question

Find the value of x and give reasoning in the following image

Answer 1

Explanation:

m<DCB + m<CBA = 180° (co-interior angles)

or, 54° + m<CBA = 180°

so, m<CBA = 180° - 54° = 126°

Now,

m<CBA + m<FAB + X = 180° (sum of interior angles of triangle)

or, 126° + 14° + X = 180°

or, X = 180° - 140°

so, X = 40°

Answer 2

angleB+angleC=180° (since AB and DC are parallel and intersected by the transversal BC)

therefore, subtracting, angle B is 126°

3 angles of triangles also makes a 180°.

So, 14°+x+126°=180°

x= 180°- 140°

x=40°