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Question 1 of 5
Use the given information to find
m/_PQW
(Chapter 2)
Find
m/_PQW if
m/_WQR=134 x,
m/_PQR=169^(@), and
m/_PQW=36 x-1.

Question $1$ of $5$ $\newline$ Use the given information to find $m \angle P Q W$ $\newline$ (Chapter $2$ ) $\newline$ Find $m \angle P Q W$ if $m \angle W Q R=134 x$ , $m \angle P Q R=169^{\circ}$ , and $m \angle P Q W=36 x-1$ .

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Write and solve direct variation equations

Full solution

Q. Question

1

of

5

\newline

Use the given information to find

m \angle P Q W

\newline

(Chapter

2

)

\newline

Find

m \angle P Q W

if

m \angle W Q R=134 x

,

m \angle P Q R=169^{\circ}

, and

m \angle P Q W=36 x-1

.

Identify Relationship: Identify the relationship between the angles. $\newline$ Since angles $PQW$ , $WQR$ , and $PQR$ are connected and $PQR$ is the full angle, we can say that $m/_{PQR} = m/_{PQW} + m/_{WQR}$ .
Substitute Given Values: Substitute the given values into the equation. $\newline$ $m/_{PQR} = 169$ degrees, $m/_{WQR} = 134x$ , and $m/_{PQW} = 36x - 1$ . $\newline$ So, $169 = (36x - 1) + 134x$ .
Combine Like Terms: Combine like terms to solve for $x$ . $169 = 36x - 1 + 134x$ $169 = 170x - 1$
Add to Isolate Terms: Add $1$ to both sides of the equation to isolate the terms with $x$ . $\newline$ $169 + 1 = 170x - 1 + 1$ $\newline$ $170 = 170x$
Divide to Solve for $x$ : Divide both sides by $170$ to solve for $x$ . $\newline$ $\frac{170}{170} = \frac{170x}{170}$ $\newline$ $1 = x$
Substitute x Back: Substitute $x$ back into the expression for $m/_{PQW}$ . $\newline$ $m/_{PQW} = 36x - 1$ $\newline$ $m/_{PQW} = 36(1) - 1$ $\newline$ $m/_{PQW} = 36 - 1$ $\newline$ $m/_{PQW} = 35$

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