Question

if $uv = ux = 97$, $mangle uwv = p + 45^circ$, and $mangle uwx = 6p$, what is $mangle uwv$?
$mangle uwv = \square ^\circ$

Explanation:

Step1: Identify angle relationship

$\angle UWV$ and $\angle UWX$ are congruent (since $UV=UX$, $WU$ is common, and both triangles are right triangles, so by HL congruence, the corresponding angles are equal). Thus:
$p + 45^\circ = 6p$

Step2: Solve for $p$

Subtract $p$ from both sides:
$45^\circ = 5p$
Divide both sides by 5:
$p = \frac{45^\circ}{5} = 9^\circ$

Step3: Calculate $m\angle UWV$

Substitute $p=9^\circ$ into $m\angle UWV = p + 45^\circ$:
$m\angle UWV = 9^\circ + 45^\circ$

Answer:

$54^\circ$