Question

If an angle is acute, then the measure of its complement must be greater than the measure of its supplement

Answer 1

This is false.
Complement equals to 90° and Supplementary equals to 180°.
Since you given angle is acute its other angle must be small than 90.
Let's say your acute angle is 35°.
Your other angle would equal 55°.

On the other hand if it was Supplementary then:
Let still use the 35° example.
35°+55° would not be Supplementary. It would have to be larger like 125°.

Answer 2

Answer:  the given statement is FALSE.

Step-by-step explanation:  We are to check whether the following statement is true or false :

"If an angle is acute, then the measure of its complement must be greater than the measure of its supplement".

Let the measure of the acute angle be x = 35°.

Then, the measure of its complement is given by

$c=90^\circ-x=90^\circ-35^\circ=55^\circ$

and the measure of the supplement is given by

$s=180^\circ-x=180^\circ-35^\circ=145^\circ.$

Therefore, we get

s > c.

Thus, the given statement is FALSE, because the complement is less than teh supplement.