# Thread: Find Measure of Angle C

1. ## Find Measure of Angle C

In triangle ABC, the measure of angle B is twice the measure of angle A. If the measure of angle A is subtracted from the measure of angle C, the difference is 20. Find the measure of angle C.

The book's answer is 60 degrees.

2. $\displaystyle A + B + C = 180 \; \mbox{ and } C-A=20 \; \mbox{ and } -2A+B=0$

$\displaystyle \left[\begin{matrix} 1 & 1 & 1 \\ -1 & 0 & 1 \\ 2 & -1 & 0 \end{matrix}\right] \left[\begin{matrix} A \\ B \\ B \end{matrix}\right]$

Solving this linear system of equations yields $\displaystyle C = 60$ .

3. ## twig...

Originally Posted by Twig
$\displaystyle A + B + C = 180 \; \mbox{ and } C-A=20 \; \mbox{ and } -2A+B=0$

$\displaystyle \left[\begin{matrix} 1 & 1 & 1 \\ -1 & 0 & 1 \\ 2 & -1 & 0 \end{matrix}\right] \left[\begin{matrix} A \\ B \\ B \end{matrix}\right]$

Solving this linear system of equations yields $\displaystyle C = 60$ .
I notice that you decided to use matrix algebra to show the answer. Can you set this up for me using a system of linear equations in 3 unknowns?

4. hi

Uhm, is this what you mean?

$\displaystyle \{A+B+C=180\}$
$\displaystyle \{C-A=20\}$
$\displaystyle \{-2A+B=0\}$

PS: If anyone could show the code for making a "large bracket" around all of the equations plz =)

5. ## ok...

Originally Posted by Twig
hi

Uhm, is this what you mean?

$\displaystyle \{A+B+C=180\}$
$\displaystyle \{C-A=20\}$
$\displaystyle \{-2A+B=0\}$

PS: If anyone could show the code for making a "large bracket" around all of the equations plz =)
I will use this system of linear equations in 3 variables to find the answer.