Question

choose all answers that describe the quadrilateral rstu if $rs = 31$, $st = 44$, $tu = 55$, $ur = 67$, $mangle r = 145^circ$, $mangle s = 45^circ$, $mangle t = 143^circ$, and $mangle u = 27^circ$.
answer attempt 1 out of 10
parallelogram
quadrilateral
rectangle
rhombus
square
trapezoid

Explanation:

Step1: Verify quadrilateral angle sum

Check if total angles = $360^\circ$
$\angle R + \angle S + \angle T + \angle U = 145^\circ + 45^\circ + 143^\circ + 27^\circ = 360^\circ$

Step2: Check parallelogram properties

Opposite sides/angles must be equal:
$RS=31
eq TU=55$, $UR=67
eq ST=44$; $\angle R=145^\circ
eq \angle T=143^\circ$, $\angle S=45^\circ
eq \angle U=27^\circ$

Step3: Check rectangle/rhombus/square

These require parallelogram properties (ruled out in Step2)

Step4: Check trapezoid properties

Requires at least one pair of parallel sides (consecutive angles supplementary):
$\angle R + \angle S = 145^\circ+45^\circ=190^\circ
eq180^\circ$, $\angle S + \angle T=45^\circ+143^\circ=188^\circ
eq180^\circ$, $\angle T + \angle U=143^\circ+27^\circ=170^\circ
eq180^\circ$, $\angle U + \angle R=27^\circ+145^\circ=172^\circ
eq180^\circ$

Answer:

Quadrilateral