Question

what is the value of c? c - 37° c c - 31° c = °

Explanation:

Step1: Apply angle - sum property of a triangle

The sum of interior angles of a triangle is 180°. For the large triangle, we have the equation: $(c - 37)+c+(c - 31)=180$.

Step2: Simplify the left - hand side of the equation

Combine like terms: $c-37 + c + c-31=3c-(37 + 31)=3c - 68$. So, $3c-68 = 180$.

Step3: Solve for c

Add 68 to both sides of the equation: $3c=180 + 68=248$. Then divide both sides by 3: $c=\frac{248}{3}\approx82.67$. But if we consider the exterior - angle property. The exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. Let's assume the correct approach using the exterior - angle property. The exterior angle $c$ is equal to the sum of the two non - adjacent interior angles of the smaller triangle formed. So $c=(c - 37)+(c - 31)$.

Step4: Expand and solve the equation

Expand the right - hand side: $c=c - 37+c - 31$. Combine like terms: $c = 2c-68$. Subtract $c$ from both sides: $0=2c - c-68$. So $c = 68$.

Answer:

$68$