Find Measure of Angle C

**magentarita** · May 3rd 2009, 12:24 PM

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.

My answer is 120 degrees.

The book's answer is 60 degrees.

**Twig** · May 3rd 2009, 12:33 PM

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

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

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

**magentarita** · May 3rd 2009, 02:40 PM

Originally Posted by Twig

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

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

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

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?

**Twig** · May 4th 2009, 10:16 AM

hi

Uhm, is this what you mean?

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

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

**magentarita** · May 4th 2009, 09:24 PM

Originally Posted by Twig

hi

Uhm, is this what you mean?

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

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.

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