(a) 1 Mark
(b) Framing the equation: 1 Mark
     Solution: 1 Mark
(a) Since it is a triangle, the perimeter of a triangle is equal to the sum of all the sides of the triangle.
     So, $x+(x+3)+41=86$
     $\Rightarrow 2x+44=86$
     $\Rightarrow 2x=42$
 
    $\Rightarrow x=21$.
(b) Let the base angle be $b^{\circ }$
     Let the vertex angle be $a^{\circ }$
    In an isosceles triangle base angles are equal.
    $\therefore a^{\circ }+b^{\circ }+b^{\circ }={180}^{\circ }$
    $2b^{\circ }+b^{\circ }+b^{\circ }={180}^{\circ }\Rightarrow$ Given that vertex angle is twice the base angle.
    $\therefore 4b^{\circ }={180}^{\circ }$
    $b^{\circ }=(\frac{180}{4}{)}^{\circ }$
    $b^{\circ }={45}^{\circ }$