The measure of the smaller supplementary angle is [tex]\[67.5{}^\circ \][/tex].
What is supplementary angle?
In mathematics, the term supplementary refers to angles that combine to form a straight angle. When two angles add up to 180 degrees, they are considered to be supplementary angles. If one of the angles is acute and the other is obtuse, the two angles are considered supplementary, the angles are both right angles.
We have to find the smallest supplementary angle.
For two angles to be supplementary, their sum should be equal[tex]${{\pi }^{c}}$[/tex] or [tex]$180{}^\circ $[/tex].
So,
[tex]$\widehat{A}+\widehat{B}=180$[/tex]
[tex]$\frac{\widehat{A}}{\widehat{B}}=\frac{5}{3}$[/tex]
[tex]$\therefore \widehat{A}=\left( \frac{5}{5+3} \right)\cdot 180$[/tex]
[tex]$=112.5$[/tex]
So, the largest supplementary angle is [tex]$112.5{}^\circ $[/tex].
Now,
[tex]$\widehat{B}=\left( \frac{3}{5+3} \right)\cdot 180$[/tex]
[tex]$=67.5$[/tex]
Hence, the smaller angle is [tex]\[67.5{}^\circ \][/tex].
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