Question

How do I solve this geometry question?

Angle ABD and angle BDE are supplementary. Find the measures of both angles.

m angle ABD =5x degrees, m angle BDE = (17x-18)degrees? can someone explain it to me?

Answer 1

Supplementary means 180 degrees. Therefore, if you add angle ABD and angle BDE they will add to 180 degrees. Here is how you can do this:

5x+17x-18=180 This represents the two angles that add to 180 degrees
22x-18=180
22x=180+18
22x=198
x=9 Substitute this number into the angles:

angle ABD=5x
angle ABD=(5)(9)=45 degrees

angle BDE=17x-18
angle BDE=(17)(9)-18
angle BDE=153-18=135 degrees

Therefore, angle ABD=45 degrees and angle BDE=135 degrees

Answer 2

can you help me with this one?
angle ABD and angle BDC are complementary. Find the measures of both angles.

m angle ABD = (5y+1)degrees, m angle BDC = (3y-7) degrees

Answer 3

Complementary means 90 degrees. When you add angle ABD and angle BDC, they will add to 90 degrees.

angle ABD+angleBDC=90 degrees
5y+1+3y-7=90
8y-6=90
8y=96
y=12

angle ABD=5y+1
angle ABD=(5)(12)+1
angle ABD=60+1
angle ABD=61 degrees

angle BDC=3y-7
angle BDC=(3)(12)-7
angle BDC=36-7
angle BDC=29 degrees