Question

Find the value of x in each case:

Answer 1

Answer:

x = 11°

4x = 44°

Step-by-step explanation:

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

BF is transversal.

$\angle BFG + \angle BFE = 180\degree\\.. (straight \: line \: \angle 's) \\ + \angle BFE = 180\degree\\\angle BFE = 180\degree-147\degree \\\angle BFE = 33\degree$

$\angle BED$ is exterior angle of $\angle EBF$

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

$m\angle BED = m\angle EBF + \angle BFE \\4x = x + 33\degree \\4x - x = 33\degree \\3x = 33\degree \\x = \frac{33}{3}\\\huge \purple {\boxed {x = 11\degree}} \\4x = 4\times 11\degree \\\huge \orange{\boxed {4x = 44\degree}}$