Question

The size of the obtuse angle of a rhombus is twice the size of its acute angle. Find the acute angle.​

Answer 1

Answer:

Step-by-step explanation:Let the rhombus be with Angles A,B,C,D

Let the Acute angle A be x

Let the Obtuse angle B = 2x +30

We know that opposite angles in a rhombus are equal.

So

Angle A = Angle C = x

Angle B = Angle D = 2x+30

We also know that the sum of all interior angles in a polygon is - (2n-4) x 90°(90 degree), where n is number of sides.

There are 4 sides in a rhombus, Hence, (2x4–4)x 90° = 4x90° = 360°, so the sum of all angles of rhombus will be 360°.

Now just put the values.

Angle A + Angle B + Angle C + Angle D= 360°

x + (2x+30) + x + (2x+30) = 360°

x+2x+30+x+2x+30 =360°

6x+ 60= 360°

6x = 360°–60°= 300

x= 300°/6

x= 50°

So the two acute angles are 50° and 50°

If x = 50°

Then 2x+30= 2(50)+30 = 100+30

= 130°

Hence, Angle A= Angle C= 50° is the acute angle.

Angle B= Angle D= 130° is the obtuse angle.