Question

what are the values of c and t?

c =

t =

Explanation:

Step1: Use the exterior angle theorem

The exterior angle theorem states that an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. So, \(t - 50=(c + 12)+(2c-24)\). Also, since \(t-50\) and \(c + 44\) are supplementary (they form a linear pair), \(t-50+(c + 44)=180\).
First, simplify the equation from the exterior angle theorem: \(t-50=3c - 12\), so \(t=3c+38\).

Step2: Substitute \(t\) into the supplementary - angle equation

Substitute \(t = 3c + 38\) into \(t-50+(c + 44)=180\).

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Step3: Find the value of \(t\)

Substitute \(c = 37\) into \(t=3c + 38\).
\(t=3\times37+38=111 + 38=149\)

Answer:

\(c = 37\), \(t = 149\)