Question

the diagram shows a triangle.
what is the value of c?
c = □°

Explanation:

Step1: Use the triangle angle sum property

The sum of angles in a triangle is \(180^{\circ}\). So, \((c - 47^{\circ})+105^{\circ}+41^{\circ}=180^{\circ}\).

Step2: Simplify the left - hand side

First, add the known angles: \(105^{\circ}+41^{\circ}=146^{\circ}\). Then the equation becomes \(c - 47^{\circ}+146^{\circ}=180^{\circ}\), which simplifies to \(c + 99^{\circ}=180^{\circ}\).

Step3: Solve for \(c\)

Subtract \(99^{\circ}\) from both sides: \(c=180^{\circ}-99^{\circ}\).

Answer:

\(81\)