24. If one angle of a parallelogram is 24° less than twice the smallest angle
then the largest angle of the parallelogram is
(b) 102°
(c) 1129
(d) 1360
(a) 68°
Answers
Answer :
The largest angle = 112°
Step-by-step explanation :
Given :
One angle of a parallelogram is 24° less than twice the smallest angle
To find :
the largest angle of the parallelogram
Solution :
Let the smallest angle be x°
In a parallelogram, the opposite angles are equal.
So, two out of four angles will be the smallest angles and the other two will be largest angles.
As given, one angle of a parallelogram is 24° less than twice the smallest angle. That angle will be the largest angle.
largest angle = (2x - 24)°
Thus, the angles of the parallelogram will be x° , (2x - 24)° , x° and (2x - 24)°
Also, in a parallelogram, the adjacent angles are supplementary angles. i.e., the sum of the adjacent angles = 180°
Here, smallest and largest angles are adjacent.
x° + (2x - 24)° = 180°
3x° - 24° = 180°
3x° = 180° + 24°
3x° = 204°
x° = 204°/3
x° = 68°
The smallest angle = 68°
The largest angle = 2(68°) - 24°
= 136° - 24°
= 112°
Therefore, the required largest angle of the parallelogram = 112°
Answer:
Answer :
The largest angle = 112°
Step-by-step explanation :
Given :
One angle of a parallelogram is 24° less than twice the smallest angle
To find :
the largest angle of the parallelogram
Solution :
Let the smallest angle be x°
In a parallelogram, the opposite angles are equal.
So, two out of four angles will be the smallest angles and the other two will be largest angles.
As given, one angle of a parallelogram is 24° less than twice the smallest angle. That angle will be the largest angle.
largest angle = (2x - 24)°
Thus, the angles of the parallelogram will be x° , (2x - 24)° , x° and (2x - 24)°
Also, in a parallelogram, the adjacent angles are supplementary angles. i.e., the sum of the adjacent angles = 180°
Here, smallest and largest angles are adjacent.
x° + (2x - 24)° = 180°
3x° - 24° = 180°
3x° = 180° + 24°
3x° = 204°
x° = 204°/3
x° = 68°
The smallest angle = 68°
The largest angle = 2(68°) - 24°
= 136° - 24°
= 112°
Therefore, the required largest angle of the parallelogram = 112°