Angle between the curves is the acute angle between the tangents at the point of intersection.

y = 10 $$-$$ x² (for curve 1)

and y = 2 + x² (for curve 2)

$$ \therefore $$  10 $$-$$ x² = 2 + x²

$$ \Rightarrow $$  2x² = 8

$$ \Rightarrow $$  x² = 4

$$ \Rightarrow $$  x = 2, $$-$$ 2

$$ \therefore $$  points of intersection (2, 6) and ($$-$$ 2, 6)

$${{dy} \over {dx}}$$ for curve 1 = $$-$$ 2x

$$ \therefore $$  Slope(m₁) of curve 1 is = $$-$$ 2(2) = $$-$$ 4

$${{dy} \over {dx}}$$ for curve 2 = 2x

$$ \therefore $$  slope (m₂) of curve 2 = 2 $$ \times $$ 2 = 4

$$ \therefore $$  tan$$\theta $$ = $$\left| {{{{m_1} - {m_2}} \over {1 + {m_1}{m_2}}}} \right|$$

= $$\left| {{{ - 4 - 4} \over {1 + \left( { - 16} \right)}}} \right|$$

= $${8 \over {15}}$$