Question

5Two consecutive angles of parallelogram are in the ratio 2:3. Find the smaller angle please send with solution I will mark brainiest ​

Answer 1

Answer:

The answer is $72^\circ$

Step-by-step explanation:

• Concept : Consecutive angles of a parallelogram are supplementary

Since consecutive angles are in the ratio 2:3

So let these angles be $2x$ and $3x$

Now using above concept : $2x+3x=180^\circ$

                                            $\Rightarrow 5x=180^\circ$

                                           $\Rightarrow x=\dfrac{180^\circ}{5}=36^\circ$

Thus the angles are $2x=72^\circ$ and $3x=108^\circ$

Therefore the smaller angle is $72^\circ$

Answer 2

Answer:

Given :-

• Two consecutive angles of a parallelogram are in the ratio of 2 : 3.

To Find :-

• What is the smaller angle of a parallelogram.

Solution :-

Let,

$\mapsto \bf First\: Angle_{(Parallelogram)} =\: 2x$

$\mapsto \bf Second\: Angle_{(Parallelogram)} =\: 3x$

As we know that :

$\footnotesize \bigstar \: \sf\boxed{\bold{\pink{Sum\: of\: two\: consecutive\: angles_{(Parallelogram)} =\: 180^{\circ}}}}\: \: \bigstar$

According to the question by using the formula we get,

$\implies \sf 2x + 3x =\: 180^{\circ}$

$\implies \sf 5x =\: 180^{\circ}$

$\implies \sf x =\: \dfrac{\cancel{180^{\circ}}}{\cancel{5}}$

$\implies \sf\bold{\purple{x =\: 36^{\circ}}}$

Hence, the required angles of a parallelogram are :

✯ First Angle Of Parallelogram :-

$\mapsto \sf First\: Angle_{(Parallelogram)} =\: 2x$

$\mapsto \sf First\: Angle_{(Parallelogram)} =\: 2 \times 36^{\circ}$

$\mapsto \sf\bold{\red{First\: Angle_{(Parallelogram)} =\: 72^{\circ}}}$

✯ Second Angle Of Parallelogram :

$\mapsto \sf Second\: Angle_{(Parallelogram)} =\: 3x$

$\mapsto \sf Second\: Angle_{(Parallelogram)} =\: 3 \times 36^{\circ}$

$\mapsto \sf\bold{\red{Second\: Angle_{(Parallelogram)} =\: 108^{\circ}}}$

$\therefore$ The smaller angle of a parallelogram is 72° .