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

Complementary Angles Equation: Since /_1 and /_2 are complementary angles, their measures add up to 90 degrees. Mathematically, this is represented as m/_1 + m/_2 = 90^(@). Substitute the given expressions for m/_1 and m/_2 into the equation. (x+18)^(@) + (3x+12)^(@) = 90^(@).Combine Like Terms: Combine like terms to solve for x. x + 18 + 3x + 12 = 90 4x + 30 = 90Isolate x: Subtract 30 from both sides to isolate the term with x. 4x + 30 - 30 = 90 - 30 4x = 60Solve for x: Divide both sides by 4 to solve for x. 4x / 4 = 60 / 4 x = 15Substitute x into m/_1: Now that we have the value of x, substitute it back into the expression for m/_1 to find the measure of /_1. m/_1 = (x+18)^(@) m/_1 = (15+18)^(@) m/_1 = 33^(@)

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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
/_1.
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 $\angle 1$ . $\newline$ Answer:

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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 1

\newline

Answer:

Complementary Angles Equation: Since $\angle 1$ and $\angle 2$ are complementary angles, their measures add up to $90$ degrees. $\newline$ Mathematically, this is represented as $m\angle 1 + m\angle 2 = 90^{\circ}$ . $\newline$ Substitute the given expressions for $m\angle 1$ and $m\angle 2$ into the equation. $\newline$ $(x+18)^{\circ} + (3x+12)^{\circ} = 90^{\circ}$ .
Combine Like Terms: Combine like terms to solve for $x$ . $x + 18 + 3x + 12 = 90$ $4x + 30 = 90$
Isolate x: Subtract $30$ from both sides to isolate the term with $x$ . $\newline$ $4x + 30 - 30 = 90 - 30$ $\newline$ $4x = 60$
Solve for x: Divide both sides by $4$ to solve for x. $\newline$ $\frac{4x}{4} = \frac{60}{4}$ $\newline$ $x = 15$
Substitute $x$ into $m/_{1}$ : Now that we have the value of $x$ , substitute it back into the expression for $m/_{1}$ to find the measure of $/_{1}$ .
$m/_{1} = (x+18)^{\circ}$
$m/_{1} = (15+18)^{\circ}$
$m/_{1} = 33^{\circ}$