Question

2. 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

Answer:

Measures of the angles are 68⁰ and 112⁰

Step-by-step explanation:

Let the smallest angle be x

Let the other angle be y

Given:

y + 24 = 2x

=> 2x - y = 24 ----- (I)

x + y + x + y = 360⁰ (Sum of all angles of a quadrilateral = 360⁰; opposite angles of a parallelogram are equal)

=> 2x + 2y = 360⁰

=> x + y = 180 ------ (II) (dividing the equation by 2)

Add equations I and II

2x - y = 24

(+) x + y = 180

-------------------

3x = 204

=> x = 204/3 = 68⁰

And y = 180 - x

=> 180 - 68

=> 112⁰

Hope this helped