Question

Using the information, given in each of the following figures, find the value of $a$.

• A. $9$
• B. $7$
• C. $10$
• D. $8$

Answer 1

The correct option is A $9$

Name the inner triangle as ABC and outer as ADE, such that $AB=AC$
$AD=2a+2$ and $AE=7b-1$
$\angle ABC=\angle ACB$ (Given)
$180-\angle ABC=180-\angle ACB$
$\angle ABD=\angle ACE$ (I)
Now, In $△ABD$ and $△ACE$
$\angle DAB=\angle EAC$ (Given)
$AB=AC$ (Given)
$\angle ABD=\angle ACE$ (From I)
Thus, $△ABD\cong △ACE$ (ASA rule)
Hence, $BD=CE$ (By cpct)
$a=3b$
$AD=AE$ (By cpct)
$2a+2=7b-1$
Put $a=3b$
$2\left(3b\right)+2=7b-1$
$6b+2=7b-1$
$b=3$
Hence, $a=3b=9$