Answer :
Answer:
Step-by-step explanation:
we know that If two angles are complementary, then their sum is equal to 90 degrees
Letx -----> the measure of an angle
y-----> the measure of he other angle
we know thatx+y=90 -----> y=90
-x -----> equation
Ax=y+54 ----> equation
Bsubstitute equation B in equation A and solve for yy=90-(y+54)
y=90-y-542y=36y=18°
Find the value of xx=y+54 -----> x=18+54=72°
thereforeThe measure of the angles are 72 degrees and 18 degrees
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[tex]\blue{\textsf{\textbf{\underline{\underline{Question:-}}}}[/tex]
An angle measures 54º more than the measure of its supplementary angle. What is the measure of each angle?
[tex]\blue{\textsf{\textbf{\underline{\underline{Answer:-}}}}[/tex]
Angle Measurements:- 63º and 117º
[tex]\blue{\textsf{\textbf{\underline{\underline{How\:to\:Solve:-}}}}[/tex]
Supplementary angles add up to 180º.
Now, let the unknown angle be n.
Set up an equation:-
[tex]\bigstar[/tex] [tex]\textsf{n+n+54=180}[/tex] (remember, supplementary angles add up to 180)
Add the n's :
[tex]\textsf{2n+54=180}[/tex]
Subtract 54 on both sides:
[tex]\textsf{2n=126}[/tex]
Divide by 2 on both sides:
[tex]\textsf{n=63\textdegree}[/tex]
Now, add 54 to find the other angle:
63+54=117
Check:-
We can easily check our work by adding the two angles together and seeing whether or not we end up with 180º.
[tex]\textsf{63+117=180}[/tex]
[tex]\textsf{180=180}\LARGE\checkmark[/tex]
LHS=RHS (Left-Hand Side = Right-Hand Side)
Hence, the angles are 63 and 117. [tex]\checkmark[/tex]
Good luck.
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