Missing angles/ find the missing angles

Question

In a triangle, the measure of the third angle is 3 more than twice the measure of the second angle. The measure of the first angle is 24 more than twice the measure of the third angle. Find the measure of each angle.

Answer 1

Ariel,

 

Let's label the angles a, b and c.

 

In a triangle, the sum of the angles equals 180: a + b + c = 180  (first equation)

 

The 3rd angle is 3 more than twice the measure of the second angle: c = 2b + 3 (second equation)

 

The first angle is 24 more than twice the measure of the third angle: a = 2c + 24 (third equation)

 

You now have 3 equations and 3 variables:

a + b + c = 180

     2b - c = -3

a       -2c = 24

 

Multiply the third equation by -1 and you will get -a + 2c = -24

 

Add the first and third equation and you will get b + 3c = 156

 

Multiply the second equation by 3 and you will get 6b - 3c = -9

 

You now have a system of 2 equations: b + 3c = 156 and 6b - 3c = -9; if you add those 2 equations, you will get 7 b = 147 and therefore b = 21

 

Substitute the value of b in the original second equation: c = 2(21) + 3 = 42 + 3 = 45

Substitute the value of c in the original third equation: a = 2(45) + 24 = 90 + 24 = 114

 

If you add a + b + c = 114 + 21 + 45 = 180

 

Hope it helps