/_1 and /_2 are complementary angles. If m/_1=(4x+7)^(@) and m/_2=(x+28)^(@), then find the measure of /_2. Answer:

Set up equation: Complementary angles add up to 90 degrees. Set up the equation using the given expressions for m/_1 and m/_2. m/_1 + m/_2 = 90° (4x + 7)° + (x + 28)° = 90°Combine like terms: Combine like terms to solve for x. 4x + x + 7 + 28 = 90 5x + 35 = 90Isolate x term: Subtract 35 from both sides to isolate the term with x. 5x + 35 - 35 = 90 - 35 5x = 55Find value of x: Divide both sides by 5 to find the value of x. 5x / 5 = 55 / 5 x = 11Substitute x back: Now that we have the value of x, substitute it back into the expression for m/_2 to find the measure of /_2. m/_2 = (x + 28)° m/_2 = (11 + 28)° m/_2 = 39°

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/_1 and
/_2 are complementary angles. If
m/_1=(4x+7)^(@) and
m/_2=(x+28)^(@), then find the measure of
/_2.
Answer:

$\angle 1$ and $\angle 2$ are complementary angles. If $\mathrm{m} \angle 1=(4 x+7)^{\circ}$ and $\mathrm{m} \angle 2=(x+28)^{\circ}$ , then find the measure of $\angle 2$ . $\newline$ Answer:

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Full solution

\angle 1

and

\angle 2

are complementary angles. If

\mathrm{m} \angle 1=(4 x+7)^{\circ}

and

\mathrm{m} \angle 2=(x+28)^{\circ}

, then find the measure of

\angle 2

\newline

Answer:

Set up equation: Complementary angles add up to $90$ degrees. Set up the equation using the given expressions for $m/\_1$ and $m/\_2$ . $m/\_1 + m/\_2 = 90°$ $(4x + 7)° + (x + 28)° = 90°$
Combine like terms: Combine like terms to solve for $x$ . $4x + x + 7 + 28 = 90$ $5x + 35 = 90$
Isolate x term: Subtract $35$ from both sides to isolate the term with $x$ . $\newline$ $5x + 35 - 35 = 90 - 35$ $\newline$ $5x = 55$
Find value of x: Divide both sides by $5$ to find the value of x. $\newline$ $\frac{5x}{5} = \frac{55}{5}$ $\newline$ $x = 11$
Substitute $x$ back: Now that we have the value of $x$ , substitute it back into the expression for $m/_{2}$ to find the measure of $/_{2}$ .
$m/_{2} = (x + 28)^{\circ}$
$m/_{2} = (11 + 28)^{\circ}$
$m/_{2} = 39^{\circ}$