Question

what is the value of c? c + 11° c + 12° c + 42°

Explanation:

Step1: Apply exterior - angle theorem

The exterior - angle of a triangle is equal to the sum of the two non - adjacent interior angles. So, $c + 42^{\circ}=(c + 11^{\circ})+(c + 12^{\circ})$.

Step2: Simplify the right - hand side

$c + 42^{\circ}=c + 11^{\circ}+c + 12^{\circ}=2c+23^{\circ}$.

Step3: Solve for c

Subtract c from both sides: $42^{\circ}=c + 23^{\circ}$. Then subtract 23° from both sides: $c=42^{\circ}-23^{\circ}=19^{\circ}$.

Answer:

$19^{\circ}$