/_1 and /_2 are complementary angles. If m/_1=(x+18)^(@) and m/_2=(3x+12)^(@), then find the measure of /_2. Answer:

Definition of Complementary Angles: Understand the definition of complementary angles. Complementary angles are two angles whose measures add up to 90 degrees.Equation Setup: Set up the equation based on the definition of complementary angles. Since angle 1 and angle 2 are complementary, we have: m/∠1 + m/∠2 = 90° Substitute m/∠1 with (x+18)° and m/∠2 with (3x+12)°. (x+18)° + (3x+12)° = 90°Combine Terms and Solve: Combine like terms and solve for x. x + 18 + 3x + 12 = 90 4x + 30 = 90Subtract and Solve for x: Subtract 30 from both sides of the equation. 4x + 30 - 30 = 90 - 30 4x = 60Divide to Find x Value: Divide both sides by 4 to find the value of x. 4x / 4 = 60 / 4 x = 15Substitute x Value: Substitute the value of x back into the expression for m/∠2 to find its measure. m/∠2 = (3x+12)° m/∠2 = (3(15)+12)° m/∠2 = (45+12)° m/∠2 = 57°

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/_1 and
/_2 are complementary angles. If
m/_1=(x+18)^(@) and
m/_2=(3x+12)^(@), then find the measure of
/_2.
Answer:

$\angle 1$ and $\angle 2$ are complementary angles. If $\mathrm{m} \angle 1=(x+18)^{\circ}$ and $\mathrm{m} \angle 2=(3 x+12)^{\circ}$ , then find the measure of $\angle 2$ . $\newline$ Answer:

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Algebra 2

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Full solution

\angle 1

and

\angle 2

are complementary angles. If

\mathrm{m} \angle 1=(x+18)^{\circ}

and

\mathrm{m} \angle 2=(3 x+12)^{\circ}

, then find the measure of

\angle 2

\newline

Answer:

Definition of Complementary Angles: Understand the definition of complementary angles. Complementary angles are two angles whose measures add up to $90^\circ$ .
Equation Setup: Set up the equation based on the definition of complementary angles. $\newline$ Since angle $1$ and angle $2$ are complementary, we have: $\newline$ $m/\angle1 + m/\angle2 = 90^\circ$ $\newline$ Substitute $m/\angle1$ with $(x+18)^\circ$ and $m/\angle2$ with $(3x+12)^\circ$ . $\newline$ $(x+18)^\circ + (3x+12)^\circ = 90^\circ$
Combine Terms and Solve: Combine like terms and solve for $x$ . $x + 18 + 3x + 12 = 90$ $4x + 30 = 90$
Subtract and Solve for x: Subtract $30$ from both sides of the equation. $\newline$ $4x + 30 - 30 = 90 - 30$ $\newline$ $4x = 60$
Divide to Find x Value: Divide both sides by $4$ to find the value of x. $\newline$ $\frac{4x}{4} = \frac{60}{4}$ $\newline$ $x = 15$
Substitute x Value: Substitute the value of $x$ back into the expression for $m/\angle2$ to find its measure. $\newline$ $m/\angle2 = (3x+12)^\circ$ $\newline$ $m/\angle2 = (3(15)+12)^\circ$ $\newline$ $m/\angle2 = (45+12)^\circ$ $\newline$ $m/\angle2 = 57^\circ$