Polygons and Angles

BG is transversal of parallel lines CJ and HF. So CDE is 140. DGH is 140 too because they're alternate interior angles and alternate interior angles are congruent.

EDJ is 40 because FGE and EDJ are alternate interior angles. BCD is also isosceles. CDB is 40 because CDB and EDJ are vertical angles. So, DBC is 40 too and C=180-40-40=100.

BDM is 90. DBA is also 90 because MD and AB are parallel lines. Angle CDB+MDB=130. LAB is 130 too because they are opposite with D. CBD+ABD=130 too. LMD is 130 also. L is 100

to prove I am right, a hexagon's interior angles sum up to 720 degrees. 100+130+130+130+130+100=720

We can say that AP is a straight line because it has a parallel. MLK=30. KLP=180-100-30=50. Angle P is 70. LKP=180-70-50=60. KLMDJ is a pentagon that means that its interior angles sum up to 540 degrees.

Measures of the angles of pentagon KLMDJ

K=tKL is the exterior angle of triangle KLP and it is equal to 120 because LPK+KLP=120. (a measure of an exterior angles is the sum of its remote interior angles).

L= 30 (given)

M=360-130=230.

D=BDJ and CDG are vertical angles and vertical angles are congruent. BDJ=BDM+MDJ so MDJ=BDJ-BDM which is 140-90=50

point J/ angle t=AP and FH are parallel. CJ and FH are parallel. AP and CJ are parallel (Transitivity). P and t are Consecutive interior angles so they sum up to 180. t=180-P so t=180-70=110 (though t in the image looks like acute angle).

120+30+230+50+110=540

r+u+s+t+Q+J=360

pairs of vertical angles r and s t and u J and Q

r+s+u=160

160+t=160+110=270

360-270=90

90/2=45

J=45

We are now in Pentagon JIHGD

D=40

G=140

J=45

H+I=540-40+140+45=540-225

H+I=540-225=315

Where is angle H and where is angle I.