## Geometry: Common Core (15th Edition)

a) By confirming the sum of the angle measures is 180. b) $m\angle ADB=77$, $m\angle BDC=103$
a) The Linear Pair Postulate tells us that two angles that form a linear pair are supplementary. b) Linear Pair Posulate $m\angle ADB+m\angle BDC=180$ Substitute the given values: $(3x+14)+(5x-2)=180$ Combine like terms: $8x+12=180$ Subtract 12 from each side: $8x+12-12=180-12$ $8x=168$ Divide each side by 8: $8x\div8=168\div8$ $x=21$ Substitute for x to find the measures. $m\angle ADB=3x+14=3(21)+14=63+14=77$ $m\angle BDC=5x-2=5(21)-2=105-2=103$