Question

the diagram shows a triangle. what is the value of z?

Explanation:

Step1: Use the triangle angle sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \((2z - 19)+(2z - 1)+44 = 180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(2z-19 + 2z-1+44=(2z + 2z)+(-19-1 + 44)=4z+( - 20+44)=4z + 24\).
The equation becomes \(4z+24 = 180\).

Step3: Solve for \(z\)

Subtract 24 from both sides: \(4z+24-24=180 - 24\), which gives \(4z=156\).
Divide both sides by 4: \(z=\frac{156}{4}=39\).

Answer:

\(39\)