Question

Find the measure of All the angles of a parallelogram, if one angle is 24°less than the twice of the smallest angle?

Answer 1

let the small angle be = x
Then the second angle = 2x - 24
Since the opposite angles are equal, the 4 angles will be x, 2x - 24, x, 2x - 24
So now by angle sum property,
x + 2x - 24 + x + 2x - 24 = 360
6x - 48 = 360
6x = 360 + 48
6x = 408
x = 408 / 6
x = 68
This the smallest angle is 68
the second angle = 2 (68) - 24
= 112
So, all angles are 68, 112, 68, 112.

Hope this helps!

Answer 2

Answer:

The angles are 68, 112

Step-by-step explanation:

We know that,

The sum of all the angles of a Parallelogram is 180

Let: The smallest angle of Parallelogram be 'x'

The second angle be (2x - 24)

= x + (2x - 24) = 180

= 3x - 24 = 180

= 3x = 204

= x = 204/3 = 68

= x = 68

∴ The other angle will be 2(68) - 24 = 112

∴ The angles are 68 and 112.