Question

BEG is a triangle. ABC and DEF are parallel lines. work out the size of angle x.

Answer 1

Answer:

$x=60^o$

Step-by-step explanation:

The picture of the question in the attached figure

step 1

Find the measure of angle BEG

we know that

$m\angle BED+m\angle BEG+m\angle GEF=180^o$ ---->  by supplementary angles (form a linear pair)

substitute the given values

$110^o+m\angle BEG+25^o=180^o$

$m\angle BEG=180^o-135^o=45^o$

step 2

Find the measure of angle HBC

we know that

$m\angle HBC+m\angle ABH=180^o$ ---> by supplementary angles (form a linear pair)

we know that

$m\angle ABH=110^o$ ---> by corresponding angles

substitute

$m\angle HBC+110^0=180^o$

$m\angle HBC=180^o-110^o=70^o$

step 3

Find the measure of angle EBG

we know that

$m\angle EBG+m\angle GBC+m\ angle HBC=180^o$

substitute the given values

$m\angle EBG+35^o+70^o=180^o$

$m\angle EBG=180^o-105^o=75^o$

step 4

Find the measure of angle x

we know that

The sum of the interior angles in any triangle must be equal to 180 degrees

so

In the triangle BEG

$m\angle BEG+m\angle BGE+m\angle EBG=180^o$

substitute the given values

$45^o+x+75^o=180^o$

$x=180^o-120^o=60^o$