# Thread:

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.

My answer is 120 degrees.

The book's answer is 60 degrees.

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

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

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

3. ## twig...

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?

4. 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 =)

5. ## ok...

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.
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 12, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "github"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "english_confidence": 0.9169737696647644, "perplexity_flag": "middle"}