Answer
a) By confirming the sum of the angle measures is 180.
b) $m\angle ADB=77$, $m\angle BDC=103$
Work Step by Step
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.
$m\angle ADB=3x+14=3(21)+14=63+14=77$
$m\angle BDC=5x-2=5(21)-2=105-2=103$
