Question

[GEOMETRY] If m∠DEG= 5x - 4 m∠GEF=7x - 8 m∠DEH= 9y + 5 find the values of x and y

Please answer this question and tell me how to do it please.

Answer 1

we are given

DEF is a line

so, sum of angles must be 180

angle(DEG)+angle(GEF)=180

now, we can plug values

$5x-4+7x-8=180$

$12x-12=180$

$12x=192$

$x=16$.........Answer

vertically opposite angle must be equal

angle(GEF)=angle(DEH)

now, we can plug values

$9y+5=7x-8$

now, we can plug x=16

$9y+5=7*16-8$

$9y+5=104$

$9y=99$

$y=11$...................Answer