Question
Is it possible to construct a quadrilateral $ROAM$ in which $RO = 4cm, OA = 5cm, \angle\text{O}=120^\circ,\angle\text{R}=105^\circ\ \text{and}\ \angle\text{A}=135^\circ$? If not, why?
✓
Answer
Given measures are $OA = 5cm,$
$\angle\text{O}=120^\circ,\angle\text{R}=105^\circ\ \text{and}\ \angle\text{A}=135^\circ$
Here, $\angle\text{A}+\angle\text{R}+\angle\text{A}$
$= 120^\circ+ 105^\circ + 135^\circ = 360^\circ$
i.e., the sum of three angles of a quadrilateral is $360^\circ $
This is impossible, as the total sum of angles is $360^\circ $ in a quadrilateral. Hence, this quadrilateral cannot be constructed.
$\angle\text{O}=120^\circ,\angle\text{R}=105^\circ\ \text{and}\ \angle\text{A}=135^\circ$
Here, $\angle\text{A}+\angle\text{R}+\angle\text{A}$
$= 120^\circ+ 105^\circ + 135^\circ = 360^\circ$
i.e., the sum of three angles of a quadrilateral is $360^\circ $
This is impossible, as the total sum of angles is $360^\circ $ in a quadrilateral. Hence, this quadrilateral cannot be constructed.
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