Math equation

Question

In a triangle the sum of the angles is 180 degrees.  If angle A is three times Angle B and Angle C is 10 degrees more than twice Angle A.  Fin the measures of the three angles to the nearest degree

Answer 1

First lets assign each angle a variable

Angle A =A

Angle B=B 

Angle C=C

 

The first sentence says the sum of all three angles equals 180 degrees so put that into an equation. 

 

A + B + C = 180

 

Next we will relate angle A to angle B, A is three times B so we would have to multiply angle B by 3 to equal angle A so written as an equation:

 

A= 3B 

 

lets reaaragne this equation so B is by it's self. We do this by dividing both sides by 3. 

 

A/3=3B/3

A/3=B 

 

next relate angle A to angle C. C is 10 degrees more than twice A. This means to find C we would multiply A by 2 and then ADD 10 degrees, in an equation this is:

 

C=10+2A 

 

Now that we know how B and C relate to A we can plug those values back into our original equation. 

 

A + B + C =180 

A + (A/3) +(10+2A) = 180 

 

Combine like terms and solve for A

 

3A + A/3 +10 = 180 

9A/3 +A/3 +10 = 180 

10A/3 +10 =180 

10A/3 = 170

10A= 510

A= 51 

 

Now we know A is equal to 51 degrees. Lets use the equation that relates A to be to find the value of B. 

 

A =3B 

51=3B

17=B 

 

B must be 17 degrees. 

 

Now lets use the equation that relates A to C to solve for C

 

C = 10 + 2A 

C = 10 + 2(51) 

C = 10 + 102

C= 112

 

C must be equal to 112 degrees. 

 

Now we can check out answer by plugging these values back into the original equation one more time. 

 

A+B+C = 180 

51 + 17 + 112 =180 

180 = 180 

 

This is true so our answers are correct 

 

Angle A = 51 degrees 

Angle B = 17 degrees 

Angle C = 112 degrees. 

Answer 2

180 = 3x + x + 2(3x) + 10

 

In this problem, you know the 3 angles must add up to 180. To find the value of each angle select one angle to be variable x. In this problem, all angles can be related to the value of Angle B, so I chose this angle to be variable x. To solve this problem, first set 180 equal to Angle A + Angle B + Angle C. Now write each angle in terms of Angle B. Here Angle A equals 3x, Angle B equals x, and Angle C equals 2(3x) + 10. Substitute these terms and solve for x. Once you have x, simply plug this value into the equation of each angle and solve for the angles measure.]

 

I hope this helps.

Answer 3

Let angle B = x

Let angle A = 3x

Let angle C = 2(3x) + 10 = 6x + 10

 

 

These three angles add up to 180 degrees.

 

x + 3x + 6x + 10 = 180

 

10x + 10 = 180

10x = 170

   x = 17

 

Next, plug in this value of x into the three angles.

 

Angle B = 17 degress

Angle A = 3(17) = 51 degrees

Angle C = 6(17) + 10 = 102 + 10 = 112 degrees