Question

the diagram shows a triangle. what is the value of z? z = \boxed{°} submit

Explanation:

Step1: Recall triangle angle sum

The sum of angles in a triangle is \(180^\circ\). So, \(30^\circ+(z + 3)^\circ+(z - 47)^\circ=180^\circ\).

Step2: Simplify the equation

Combine like terms: \(30 + z + 3 + z - 47 = 180\) → \(2z - 14 = 180\).

Step3: Solve for z

Add 14 to both sides: \(2z = 194\). Divide by 2: \(z=\frac{194}{2}=97\).

Answer:

\(97\)