Question

the diagram shows a triangle.
(angle: 2z - 45°), (angle: 2z - 15°), (angle: 2z - 47°)
what is the value of z?
write your answer as an integer or as a decimal rounded to the nearest tenth.
z = \boxed{\space}°

Explanation:

Step1: Recall triangle angle sum

The sum of angles in a triangle is \(180^\circ\). So, \((2z - 45^\circ)+(2z - 15^\circ)+(2z - 47^\circ)=180^\circ\).

Step2: Combine like terms

Simplify the left - hand side: \(2z+2z + 2z-45 - 15-47=180\), which is \(6z-(45 + 15+47)=180\). Calculate \(45 + 15+47 = 107\), so \(6z-107 = 180\).

Step3: Solve for z

Add 107 to both sides: \(6z=180 + 107=287\). Then divide both sides by 6: \(z=\frac{287}{6}\approx47.8\).

Answer:

\(z\approx47.8\)