Question

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

Answer 1

See below

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=(1)/(2)AE`

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