BIGEST ANGEL OF A TRIANGLE IS DOUBLED OF THE SMALLEST ANGEL AND THIRED ANGEL IS HALF OF THE SUM OF THE OTHER TWO ANGEL FIND THE ANGELS

Question

BIGEST ANGEL OF A TRIANGLE IS DOUBLED OF THE SMALLEST ANGEL AND THIRED ANGEL IS HALF OF THE SUM OF THE OTHER TWO ANGEL FIND THE ANGELSgd

Answer 1

First, it is important to know that all angles in any triangle must add up to 180^o.

If we set the variable "x" as the smallest angle, we can find the values of the other two angles based on the given information.

The biggest angle is double of the smallest angle, so let's call it "2x."

The third angle is half the sum of the other two angles, so add 2x + x and multiply by 0.5.

Now put the pieces together and ensure that they add to 180.

x + 2x + 0.5(2x +x) = 180            

Solve for x to get the value of the smallest angle.

x + 2x + x + 0.5x = 180               

Combine like terms.

4.5x = 180                                  

Isolate the x.

x = (180/4.5)

x = 40.                            

The smallest angle is 40^o.

The largest angle is twice the smallest angle.  2(40) = 80^o.

The middle angle is half the sum of the other two angles. (40 + 80)(0.5) = (120)(0.5) = 60^o

Just to double check:  40^o + 80^o + 60^o = 180^o

 

Answer 2

We know that the sum of the angles of a triangle is 180 degrees. So if we let a, b, and c be the measures of the three angles, then
a + b + c = 180. 

For the sake of argument, let's assume that a is the largest angle and c is the smallest angle. Using the information they provided, we can then write the following equations
a = 2c     (The Biggest angle is double the smallest angle)

b = (a+c)/2

Now if we take these last two equations and substitute into the first, we get

(2c) + (a + c)/2 + c = 180     <=== Note that we still have a in the equation, so we need to substitute again:

(2c) + (2c + c)/2 + c = 180

Simplifying, we get 3c + 3c/2 = 180 
9c/2 = 180

Multiplying by 2/9 to clear the fraction, we get c = (180)(2/9) = 40

Since c = 40, then a = 2(40) = 80  and b = (80 + 40)/2 = 60

so the angles are 80, 60, and 40