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/_1 and
/_2 are complementary angles. If
m/_1=(6x+15)^(@) and
m/_2=(x-9)^(@), then find the measure of
/_1.
Answer:

$\angle 1$ and $\angle 2$ are complementary angles. If $\mathrm{m} \angle 1=(6 x+15)^{\circ}$ and $\mathrm{m} \angle 2=(x-9)^{\circ}$ , then find the measure of $\angle 1$ . $\newline$ Answer:

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Transformations of functions

Full solution

Q.

\angle 1

and

\angle 2

are complementary angles. If

\mathrm{m} \angle 1=(6 x+15)^{\circ}

and

\mathrm{m} \angle 2=(x-9)^{\circ}

, then find the measure of

\angle 1

.

\newline

Answer:

Set Up Equation: Complementary angles add up to $90$ degrees. We can set up an equation with the given expressions for $m/\text{angle } 1$ and $m/\text{angle } 2$ to find the value of $x$ . $\newline$ Equation: $(6x + 15) + (x - 9) = 90$
Combine Like Terms: Combine like terms in the equation. $\newline$ $6x + x + 15 - 9 = 90$ $\newline$ $7x + 6 = 90$
Isolate $x$ : Subtract $6$ from both sides of the equation to isolate the term with $x$ . $7x + 6 - 6 = 90 - 6$ $7x = 84$
Solve for x: Divide both sides of the equation by $7$ to solve for x. $\newline$ $\frac{7x}{7} = \frac{84}{7}$ $\newline$ $x = 12$
Substitute $x$ : Now that we have the value of $x$ , we can find the measure of angle $1$ by substituting $x$ back into the expression for $m/\text{angle } 1$ . $\newline$ $m/\text{angle } 1 = 6x + 15$ $\newline$ $m/\text{angle } 1 = 6(12) + 15$
Calculate Angle $1$ : Calculate the value of $m/\text{angle } 1$ . $\newline$ $m/\text{angle } 1 = 72 + 15$ $\newline$ $m/\text{angle } 1 = 87°$

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