Answer:
∠64° and ∠26°
Step-by-step explanation:
Complementary angles add up to 90° total (two angles).
Lets give variable values to each angle:
x= 12 more than twice the measure of the complement
y= complement
Write an equation equaling to a total of 90:
[tex]x+y=90[/tex]
Write an algebraic expression for the value of x:
[tex]12+2y[/tex]
Insert the value for x into the equation:
[tex]12+2y+y=90[/tex]
Simplify and solve for y:
[tex]12+3y=90\\\\12-12+3y=90-12\\\\3y=78\\\\\frac{3y}{3}=\frac{78}{3}\\\\ y=26[/tex]
The value of y is 26. Insert this value into the original equation and solve for x:
[tex]x+26=90\\\\x+26-26=90-26\\\\x=64[/tex]
The value of x is 64. So, the complemenatry angles are 64° and 26°.
:Done
From the given measure whose angle is 12° more than twice the measure of its complement.
The measure of the two angles is 64° and 26° respectively.
Complementary angles are angles whose sum is equal to 90°. It is usually composed of two angles complementing themselves. Hence, the term complementary angles.
Mathematically;
∴
p + q = 90° ( complemntary angles)
If one of the angles is 12 more than twice its complement;
i.e.
Let p = 12
SO, the algebraic equation for the value of p is:
12 + 2q = 90
Replacing the value of q to solve the equation, we have:
12 + 2q + q = 90
12 + 3q = 90
3q = 90 - 12
3q = 78
q = 78/3
q = 26°
From p + q = 90° ( complemntary angles)
Replacing the value of q = 26°, we have:
p + 26° = 90°
p = 90° - 26°
p = 64°
In conclusion, the measure of each angle is 64° and 26°.
Learn more about complementary angles here:
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