Answer:
m<DEB=113°
Explanation:
Hokay, so-
given m<ABH=67°, you know that
m<CBF=67° | verticle angles
and you know that:
m<ABF=m<CBH | verticle angles
--> 67°+67°+m<ABF+m<CBH=360°
134°+m<ABF+m<CBH=360°
m<ABF+m<CBH=226°
x+x=226°
2x=226°
x=113°
x=m<ABF=m<CBH=113°
m<BFE=m<CBF=67° | alt. interior angles
Since you are also given BE=BF, you know that BEF is an isos. triangle, meaning:
--> m<BEF=m<BFE=67°
now that you know what m<BEF is,
180°-m<BEF=m<DEB
180°-67°=m<DEB
m<DEB=113°
orrrrr
you could have skipped all that and just figured it out in the first half when you found x=113°, and see that
m<ABF=m<BFG | alt. int. angles
to realize that m<DEB=113° but I'm typing this in the middle of my geo RSM class so my brains pretty much shut off now qwq