Question

Adjacent angles of a parallelogram are in the ratio of $1:2$ ,find the measures of the smallest angles of parallelogram.

Answer 1

Hint- This question can be solved by knowing the concept that the sum of the adjacent angles of parallelogram is ${180^ \circ }$.

Given that the adjacent angles of a parallelogram are in the ratio of $1:2$.
Let the adjacent angles be $x$ and $2x$.
We know that the sum of the adjacent angles of the parallelogram is ${180^ \circ }$ .
$ \Rightarrow x + 2x = {180^ \circ }$
Or $3x = {180^ \circ }$
Or $x = \dfrac{{{{180}^ \circ }}}{3}$
Or $x = {60^ \circ }$
Therefore, adjacent angles are
$
  x = {60^ \circ } \\
  2x = 2 \times x \\
  2x= 2 \times {60^ \circ } \\
  2x= {120^ \circ } \\
 $
Now we have to find the measure of the smallest angle, which is ${60^ \circ }$ .
Therefore, the smallest angle is ${60^ \circ }$ .

Note-Whenever we face such types of questions the key concept is that we should know the basic things like the sum of adjacent angles of a parallelogram is ${180^ \circ }$. Like in this question we use the same concept and thus we get our desired answer.