5Two consecutive angles of parallelogram are in the ratio 2:3. Find the smaller angle please send with solution I will mark brainiest
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5Two consecutive angles of parallelogram are in the ratio 2:3. Find the smaller angle please send with solution I will mark brainiest
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Answer:
The answer is [tex]72^\circ[/tex]
Step-by-step explanation:
Since consecutive angles are in the ratio 2:3
So let these angles be [tex]2x[/tex] and [tex]3x[/tex]
Now using above concept : [tex]2x+3x=180^\circ[/tex]
[tex]\Rightarrow 5x=180^\circ[/tex]
[tex]\Rightarrow x=\dfrac{180^\circ}{5}=36^\circ[/tex]
Thus the angles are [tex]2x=72^\circ[/tex] and [tex]3x=108^\circ[/tex]
Therefore the smaller angle is [tex]72^\circ[/tex]
Answer:
Given :-
To Find :-
Solution :-
Let,
[tex]\mapsto \bf First\: Angle_{(Parallelogram)} =\: 2x[/tex]
[tex]\mapsto \bf Second\: Angle_{(Parallelogram)} =\: 3x[/tex]
As we know that :
[tex]\footnotesize \bigstar \: \sf\boxed{\bold{\pink{Sum\: of\: two\: consecutive\: angles_{(Parallelogram)} =\: 180^{\circ}}}}\: \: \bigstar\\[/tex]
According to the question by using the formula we get,
[tex]\implies \sf 2x + 3x =\: 180^{\circ}[/tex]
[tex]\implies \sf 5x =\: 180^{\circ}[/tex]
[tex]\implies \sf x =\: \dfrac{\cancel{180^{\circ}}}{\cancel{5}}[/tex]
[tex]\implies \sf\bold{\purple{x =\: 36^{\circ}}}[/tex]
Hence, the required angles of a parallelogram are :
✯ First Angle Of Parallelogram :-
[tex]\mapsto \sf First\: Angle_{(Parallelogram)} =\: 2x[/tex]
[tex]\mapsto \sf First\: Angle_{(Parallelogram)} =\: 2 \times 36^{\circ}[/tex]
[tex]\mapsto \sf\bold{\red{First\: Angle_{(Parallelogram)} =\: 72^{\circ}}}\\[/tex]
✯ Second Angle Of Parallelogram :
[tex]\mapsto \sf Second\: Angle_{(Parallelogram)} =\: 3x[/tex]
[tex]\mapsto \sf Second\: Angle_{(Parallelogram)} =\: 3 \times 36^{\circ}[/tex]
[tex]\mapsto \sf\bold{\red{Second\: Angle_{(Parallelogram)} =\: 108^{\circ}}}\\[/tex]
[tex]\therefore[/tex] The smaller angle of a parallelogram is 72° .