Given that the ratio of the measures of two supplementary angles is:
[tex]1:29[/tex]
You need to remember that, by definition, the measures of Supplementary Angles add up to 180 degrees.
Therefore, you can represent 180 degrees as:
[tex]1+29=30[/tex]
Then, you can determine that one of the angles is:
[tex]\frac{180\text{\degree}}{30}=6\text{\degree}[/tex]
And the measure of the other angle is:
[tex]180\text{\degree}-6\text{\degree}=174\text{\degree}[/tex]
Notice that the smaller angle is the one with the lowest measure.
Hence, the answer is:
[tex]6\text{\degree}[/tex]
