Answer
$36.87^{\circ}$
Work Step by Step
$\textbf u $=$\langle 1,7 \rangle$
$\textbf v $=$\langle 1,1 \rangle$
$\cos\theta$=$\frac{ \textbf u . \textbf v }{ | \textbf u | | | \textbf v | } $
$\cos\theta$=$\frac{ \langle 1,7 \rangle . \langle 1,1 \rangle }{ | \sqrt {1^2+7^2}| | | \sqrt { 1^2+1^2} | } $
$\cos\theta$=$\frac{ 1\times 1+7\times 1 }{ | \sqrt {50}| | | {\sqrt { 2} | } }$
$\cos\theta$=$\frac{ 8 }{ | \sqrt {50}| | | \sqrt { 2} | } $
$\cos\theta$=$\frac{ 8 }{ 10 }=\frac{4}{5}$
$\theta$ $=\cos^{-1}\left(\frac{4}{5}\right)=36.87^{\circ}$
