Question

Find the measure of all the angles of the parallelogram if one angle is 24 less than twice the smallest angle.

Answer 1

Hint- We know that parallelogram is a quadrilateral with opposite sides parallel, so we can say the opposite angles are also parallel that is a parallelogram consisting of two pairs with the same angle. Now, let x be the smallest angle of the parallelogram, analyze the condition, and determine the answer.

Complete step by step answer:

We know that the sum of adjacent angles of a parallelogram = 180$^\circ $
Let the smallest angle of the parallelogram be x.
Then the adjacent angle will be (2x-24).
x + (2x - 24) = 180
3x - 24 = 180
3x = 204
x = 68$^\circ $
Thus the other angle = 2x – 24 = 2(68) - 24 = 112$^\circ $
Now since it is a parallelogram the opposite angles will be equal to them
Therefore the angles are 68$^\circ $, 112$^\circ $, 68$^\circ $and 112$^\circ $.

Note- We can also find it in a simple way,
It is given that the other angle is 24° less than twice of the smallest.
So we get angle to be (2x-24°)
And same as x there must be another angle equal to 2x-24°
And the sum of all the angles of the quadrilateral is 360°.
So adding all and equating it with 360°.
We’ll get,
2x-24+2x-24+x+x=360
6x=360+48
6x=408
x=68°
(Now you know what to do.)