Question

Find the value of x in each case:

Answer 1

x = 11°

4x = 44°

Explanation:

Line BC || Line EF... (given)

BF is transversal.

`\angle BFG + \angle BFE = 180\degree\\.. (straight \: line \: \angle 's) \\</p><p> + \angle BFE = 180\degree\\</p><p>\angle BFE = 180\degree-147\degree \\</p><p>\angle BFE = 33\degree\\`

`\angle BED` is exterior angle of
`\angle EBF`

Hence, by remote interior angle theorem of triangle, we have:

`m\angle BED = m\angle EBF + \angle BFE \\</p><p>4x = x + 33\degree \\</p><p>4x - x = 33\degree \\</p><p>3x = 33\degree \\</p><p>x = (33)/(3)\\</p><p>\huge \purple {\boxed {x = 11\degree}} \\</p><p>4x = 4* 11\degree \\</p><p>\huge \orange{\boxed {4x = 44\degree}} </p><p>`