The measure of m<BDE and m<ABD are 108 and 72 degrees respectively
The sum of supplementary angles equals 180 degrees. Since m<ABD and m<BDE is supplementary, hence;
m<ABD + m<BDE = 180
3x+12 + 7x - 32 = 180
10x - 20 = 180
10x = 180 + 20
10x = 200
x = 200/10
x = 20
Get the measure of ABD:
m<ABD = 3x + 12
m<ABD = 3(20) + 12
m<ABD = 60 + 12
m<ABD = 72degrees
Get the measure of BDE:
m<BDE = 180 - m<ABD
m<BDE = 180 - 72
m<BDE = 108degrees
Hence the measure of m<BDE and m<ABD are 108 and 72 degrees respectively
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