Abcdef and ehg are regular polygons. if mhgj=220* on the exterior of the polygon, megj is congruent to mged, and mcdj=136* on the exterior of the polygon, what is the measure of gjd?

96 deg

Step-by-step explanation:

Polygon ABCDE is a regular hexagon. The sum of the measures of the interior angles is (n - 2)180 = (6 - 2)180 = 4(180) = 720. Since it's a regular hexagon, each interior angle measures 720/6 = 120 deg.

For the interior angle, m<CDE = 120

On the exterior of the polygon, m<CDJ = 136

m<CDE + m<CDJ + m<EDJ = 360

120 + 136 + m<EDJ = 360

m<EDJ + 256 = 360

m<EDJ = 104 deg

Triangle EHG is regular. The sum of the measures of the angles of a triangle is 180. For a regular triangle, each angle measures 60 deg.

m<EGH = 60

For exterior angle m<HGJ = 220

m<HGJ(exterior) + m<EGH + m<EGJ = 360

220 + 60 + m<EGJ = 360

m<EGJ + 280 = 360

m<EGJ = 80

m<EGJ = m<GED, so

m<GED = 80

Polygon DEGJ is a quadrilateral. The sum of the measures of its interior angles is 360 deg.

m<EGJ + m<GED + m<EDJ + m<GJD = 360

80 + 80 + 104 + m<GJD = 360

m<GJD + 264 = 360

m<GJD = 96 deg