In the diagram, TX is perpendicular to UW, |UX| = 1cm and |TX| = |WX|…

Explanation

In \(\Delta\) UXT, tan\(\alpha\) = \(\frac{1}{\sqrt{3}}\)

\(\alpha\) = tan^-1(\(\frac{1}{\sqrt{3}}\))

= 30^o

In \(\Delta\)WXT, tan\(\beta\) \(\frac{\sqrt{3}}{\sqrt{3}}\) = 1

\(\beta\) = tan^-1(1) = 45^o

Hence, < UTW = \(\alpha\) + \(\beta\)

= 30^o + 45^o = 75^o