Question

what is the value of c? 13c - 43° 6c + 22° 37° write your answer as an integer or as a decimal rounded to the nearest tenth. c =

Explanation:

Step1: Apply exterior - angle property

The exterior - angle of a triangle is equal to the sum of the two non - adjacent interior angles. So, \(13c - 43=(6c + 22)+37\).

Step2: Simplify the right - hand side

\((6c + 22)+37=6c+59\). So the equation becomes \(13c - 43 = 6c+59\).

Step3: Move the terms with \(c\) to one side

Subtract \(6c\) from both sides: \(13c-6c - 43=6c - 6c+59\), which simplifies to \(7c-43 = 59\).

Step4: Isolate the term with \(c\)

Add 43 to both sides: \(7c-43 + 43=59 + 43\), so \(7c=102\).

Step5: Solve for \(c\)

Divide both sides by 7: \(c=\frac{102}{7}\approx14.6\).

Answer:

\(14.6\)