Question

in your equation, ∠wvu is x. so, ( x + 5x + 18 = 8x - 15 ).
1 if ( overleftrightarrow{yz} ) bisects ( angle uvx ), find ( mangle wvu ).
a) ( 36^circ ) a pirate ship
b) ( 40^circ ) a parade float
c) ( 38^circ ) a carousel
d) ( 32^circ ) a train
e) ( 34^circ ) a trampoline

Explanation:

Step1: Set equal bisected angles

Since $\overrightarrow{YZ}$ bisects $\angle UVX$, then $m\angle UVZ = m\angle XVZ$.
$5x + 18 = 8x - 15$

Step2: Solve for $x$

Rearrange terms to isolate $x$:
$18 + 15 = 8x - 5x$
$33 = 3x$
$x = \frac{33}{3} = 11$

Step3: Find $m\angle UVZ$

Substitute $x=11$ into $5x+18$:
$m\angle UVZ = 5(11) + 18 = 55 + 18 = 73^\circ$

Step4: Find $m\angle WVU$

$\angle WVU$ and $\angle UVX$ are vertical angles, so $m\angle WVU = m\angle UVX$. Since $\angle UVX = 2\times m\angle UVZ$:
$m\angle WVU = 2\times73 = 146^\circ$? No, correct: $\angle WVU$ and $\angle YVX$ are vertical angles, $\angle YVX = 180^\circ - m\angle UVX$. Wait, correct: $\angle WVU$ is vertical to $\angle XVY$, and $\angle XVY = 180^\circ - 2\times73^\circ=34^\circ$.
Wait, correction: $\angle WVU$ is vertical to $\angle XVY$. $\angle UVX = 2\times73=146^\circ$, so $\angle XVY = 180^\circ - 146^\circ=34^\circ$, so $m\angle WVU=34^\circ$.

Answer:

E) $34^\circ$ a trampoline