Answer:
The measure of the complement of angle A is [tex]70\°[/tex]
Explanation:
we know that
If two angles are complementary, then their sum is equal to 90 degrees
If two angles are supplementary, then their sum is equal to 180 degrees
Let
x ----> the measure of angle A
(90-x) ----> the measure of the complement of angle A
(180-x) ---> the measure of the supplement of angle A
we know that
[tex]\frac{3x}{4(90-x)}=\frac{3}{14}[/tex] -----> equation A
[tex]\frac{3x}{0.5(180-x)}=\frac{3}{4}[/tex] ----> equation B
Solve equation A or equation B to determine the value of x
Solve equation A
[tex]\frac{3x}{4(x-90)}=\frac{3}{14}[/tex]
[tex]14(3x)=4(90-x)(3)\\42x=1,080-12x\\54x=1,080\\x=20[/tex]
Verify the value of x in the equation B
[tex]\frac{3(20)}{0.5(180-20)}=\frac{3}{4}[/tex]
[tex]\frac{60}{80}=\frac{3}{4}[/tex]
[tex]\frac{3}{4}=\frac{3}{4}[/tex] ---> is ok
Find out the measure of the complement of angle A
([tex]90-x)\°=(90-20)\°=70\°[/tex]
