Question

△ACE, B is the midpoint of AC and D is the midpoint of EC.

Answer 1

Answer:

See below

Step-by-step explanation:

$1.\:\:\overline{BD}||\overline{AE}$

(By Midsegment theorem)

$2.\:\:m\angle 1=48\degree\implies m\angle 4=48\degree$

($\angle 1\: \&\:\angle 4$ are alternate angles)

$3.\:\:m\angle 3=25\degree\implies m\angle 2=25\degree$

($\angle 2\: \&\:\angle 3$ are vertical angles)

$4.\:\:\overline {AE}=17\: cm\implies BD = 8.5\: cm$

(By midsegment theorem: $BD=\frac{1}{2}AE$

$5.\:\: BD=\frac{1}{2}AE\\\\\implies (3x+10)=\frac{1}{2}\times (12x+2)\\\\\implies 2(3x +10) = 12x+2\\\\\implies 6x +20= 12x+2\\\\\implies 6x - 12x = 2-20\\\\\implies -6x =-18\\\\\implies x =\frac{-18}{-6}\\\\\implies x = 3\\\\\implies \overline{BD}= (3\times 3 + 10)\\\\=(9+10)\\\\\implies \overline{BD}= (9 + 10)\\\\\implies \huge{\purple{\overline{BD}=19}}$