Question : The measure of three angles of a quadrilateral are in the ratio 1 : 2 : 3. If the sum of these three measures is equal to the measure of the fourth angle, then find the smallest angle.
Option 1: $30^\circ$
Option 2: $40^\circ$
Option 3: $60^\circ$
Option 4: $50^\circ$
Correct Answer: $30^\circ$
Solution :
Let the 1st, 2nd and 3rd angles be $x$, $2x$, and $3x$.
$\therefore$ The 4th angle = $x+2x+3x=6x$
We know that the sum of the angles of the quadrilateral is $360^\circ$.
According to the question,
$x+2x+3x+6x=360^\circ$
⇒ $12x=360^\circ$
⇒ $x=30^\circ$
Since, the smallest angle is $x$, so $x=30^\circ$
Hence, the correct answer is $30^\circ$.
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