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

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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.

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.

Last updated date: 25th May 2023

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