/_1 and /_2 are complementary angles. If m/_1=(2x+1)^(@) and m/_2=(4x+11)^(@), then find the measure of /_2. Answer:

Define Complementary Angles: Understand the definition of complementary angles. Complementary angles are two angles whose measures add up to 90 degrees.Set Up Equation: Set up the equation based on the definition of complementary angles. Since angle 1 and angle 2 are complementary, we have: m/angle 1 + m/angle 2 = 90 degrees Substitute the given expressions for m/angle 1 and m/angle 2: (2x + 1) + (4x + 11) = 90Combine Like Terms: Combine like terms in the equation. 2x + 4x + 1 + 11 = 90 6x + 12 = 90Solve for x: Solve for x. Subtract 12 from both sides of the equation: 6x + 12 - 12 = 90 - 12 6x = 78 Divide both sides by 6: x = 78 / 6 x = 13Find Angle 2: Find the measure of angle 2 using the value of x. Substitute x = 13 into the expression for m/angle 2: m/angle 2 = 4x + 11 m/angle 2 = 4(13) + 11 m/angle 2 = 52 + 11 m/angle 2 = 63 degrees

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/_1 and
/_2 are complementary angles. If
m/_1=(2x+1)^(@) and
m/_2=(4x+11)^(@), then find the measure of
/_2.
Answer:

$\angle 1$ and $\angle 2$ are complementary angles. If $\mathrm{m} \angle 1=(2 x+1)^{\circ}$ and $\mathrm{m} \angle 2=(4 x+11)^{\circ}$ , then find the measure of $\angle 2$ . $\newline$ Answer:

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Algebra 2

Transformations of functions

Full solution

\angle 1

and

\angle 2

are complementary angles. If

\mathrm{m} \angle 1=(2 x+1)^{\circ}

and

\mathrm{m} \angle 2=(4 x+11)^{\circ}

, then find the measure of

\angle 2

\newline

Answer:

Define Complementary Angles: Understand the definition of complementary angles. Complementary angles are two angles whose measures add up to $90^\circ$ .
Set Up Equation: Set up the equation based on the definition of complementary angles. $\newline$ Since angle $1$ and angle $2$ are complementary, we have: $\newline$ $m/\text{angle 1} + m/\text{angle 2} = 90$ degrees $\newline$ Substitute the given expressions for $m/\text{angle 1}$ and $m/\text{angle 2}$ : $\newline$ $(2x + 1) + (4x + 11) = 90$
Combine Like Terms: Combine like terms in the equation. $\newline$ $2x + 4x + 1 + 11 = 90$ $\newline$ $6x + 12 = 90$
Solve for x: Solve for x. $\newline$ Subtract $12$ from both sides of the equation: $\newline$ $6x + 12 - 12 = 90 - 12$ $\newline$ $6x = 78$ $\newline$ Divide both sides by $6$ : $\newline$ $x = \frac{78}{6}$ $\newline$ $x = 13$
Find Angle $2$ : Find the measure of angle $2$ using the value of $x$ . Substitute $x = 13$ into the expression for $m/\text{angle } 2$ : $m/\text{angle } 2 = 4x + 11$ $m/\text{angle } 2 = 4(13) + 11$ $m/\text{angle } 2 = 52 + 11$ $m/\text{angle } 2 = 63$ degrees