Question

Find the value of x in each case:

Answer 1

x=30 degress

Explanation:

BIG BRAIN

Answer 2

`x=30\°`

Explanation:

Find the measures of interior angles in each triangle

Triangle BGC

`m<BCG=90\°-60\°=30\°`

The measures of triangle BGC are
`90\°-60\°-30\°`

Triangle CGH

we know that

`m<BCE+m<DEC=180\°` -----> by consecutive interior angles

we have that

`m<DEC=90\°`

so

`m<BCE=90\°`

`m<GCH=90\°-m<BCG`

substitute

`m<GCH=90\°-30\°=60\°`

we have

`m<GCH=60\°`

`m<CGH=2x\°`

`m<CHG=180\°-4x`

remember that

`m<GCH+m<CGH+m<CHG=180\°`

`60\°+2x+180\°-4x=180\°`

`60\°=2x`

`x=30\°`

The measures of triangle CGH are
`60\°-60\°-60\°`

Triangle GHE

`m< EGH=90\°-2x=90-2(30\°)=30\°`

`m< GHE=4x=4(30\°)=120\°`

remember that

`m<EGH+m<GHE+m<GEH=180\°`

substitute and solve for m<GEH

`30\°+120\°+m<GEH=180\°`

`150\°+m<GEH=180\°`

`m<GEH=30\°`

The measures of triangle GHE are
`30\°-120\°-30\°`