Question

If the measure of one angle in a parallelogram is 24° less than twice the smallest angle, find all angles of the parallelogram.

Answer 1

Let's consider the smallest angle as ‘y’.

Now it's given that the other angle is 24 degrees less than twice the ‘y’. Let's consider the other angle as ‘x’. So,
x = 2y-24

We know that the opposite angles of a parallelogram are equal.
According to the angle sum property of a quadrilateral, we can write
2x+2y = 360°
2(2y - 24) +2y = 360°
4y-48+2y = 360°
6y-48=360°
On rearranging we get,
y = (360 + 48)/6 = 68°
x = 2y - 24 = 2
68-24= 112°

Hence, the angles are 68°, 68°, 112°, and 112°.