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$Tandard 7.G.5 Write and solve equations for unknown angles using facts about supplementary, complementary, vertical, and adjacent angles MP 6 Attend to precision. Directions: Complete the following problems. Show appropriate work and details to supp What is the value of x ? Write an equation. Then find the missing angle measures. {:[x=],[/_AQB=],[/_BQC=]:}$

Tandard $\newline$ $7$ .G. $5$ $\newline$ Write and solve equations for unknown angles using $\newline$ facts about supplementary, complementary, vertical, $\newline$ and adjacent angles $\newline$ MP $6$ $\newline$ Attend to precision. $\newline$ Directions: Complete the following problems. Show appropriate work and details to supp $\newline$ $1$ . What is the value of $x$ ? Write an equation. Then find the missing angle measures. $\newline$ $\begin{array}{l} x= \\ \angle A Q B= \\ \angle B Q C= \end{array}$

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Write equations of cosine functions using properties

Full solution

Q. Tandard

\newline

7

.G.

5

\newline

Write and solve equations for unknown angles using

\newline

facts about supplementary, complementary, vertical,

\newline

and adjacent angles

\newline

MP

6

\newline

Attend to precision.

\newline

Directions: Complete the following problems. Show appropriate work and details to supp

\newline

1

. What is the value of

x

? Write an equation. Then find the missing angle measures.

\newline

\begin{array}{l} x= \\ \angle A Q B= \\ \angle B Q C= \end{array}

Write equation: Since angles $AQB$ and $BQC$ are adjacent, they are supplementary and add up to $180$ degrees. $\newline$ So, we write the equation $x + (x + 10) = 180$ .
Combine like terms: Combine like terms: $2x + 10 = 180$ .
Subtract and solve: Subtract $10$ from both sides: $2x = 170$ .
Find $AQB$ measure: Divide both sides by $2$ : $x = 85$ .
Find BQC measure: Now we find the measure of angle $AQB$ by plugging in $x$ : $AQB = x = 85$ degrees.
Find BQC measure: Now we find the measure of angle $AQB$ by plugging in $x$ : $AQB = x = 85$ degrees. Next, we find the measure of angle $BQC$ by plugging in $x$ : $BQC = x + 10 = 85 + 10 = 95$ degrees.

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