Question

three angles are adjacent to each other and form 140.the largest angle is twice the smaller angle and the angle which is middle size is 24 more than the smallest. find the angles​

Answer 1

The angles are 29°, 53° and 58°

Answer 2

Answer:

Smallest: 29, Middle: 53, Largest: 58

Step-by-step explanation:

We can represent the angles in this problem using an equation.

We'll use x to represent the smallest angle, and work out other ways to represent the others.

As the largest angle is twice that of the smaller angle, we can represent the largest angle as 2x as 2x is two times x.

The middle angle is 24 more than the smallest, so we can represent that one as x + 24, since it is 24 more than the smallest.

Now we have our angles all represented with x:

Smallest angle = x

Middle = x+24

Largest = 2x

We know that they all add together to 140 so our equation is:

x+2x+(x+24) = 140

Now we can solve for x!

We can remove the brackets (addition does not change the terms) and combine the terms:

x+2x+x+24=140

4x+24=140

Next we move the 24 to the other side so we can solve for x:

4x + 24 - 24 = 140 - 24

4x = 116

Finally we divide both sides by 4:

x=29

The smallest angle is 29!

Now we can use our representations to find the other angles:

Middle angle = x+24, therefore it is 29+24 = 53

Largest angle = 2x therefore it is 2*29 = 58

58+53+29=140 so we have successfully worked out our angles!

Hope this helped!