Question

the diagram shows a triangle.
5z-14°
2z-15°
38°
what is the value of z?
write your answer as an integer or as a decimal rounded to the nearest tenth.
z = □°

Explanation:

Step1: Sum of triangle angles is \(180^\circ\)

The sum of the interior angles of a triangle is \(180^\circ\). So, we can set up the equation: \((2z - 15) + (5z - 14) + 38 = 180\).

Step2: Simplify the left - hand side

First, combine like terms: \(2z+5z-15 - 14+38=180\).
\(7z+(-15 - 14 + 38)=180\).
\(-15-14=-29\), and \(-29 + 38 = 9\). So the equation becomes \(7z+9 = 180\).

Step3: Solve for \(z\)

Subtract 9 from both sides: \(7z=180 - 9=171\).
Then divide both sides by 7: \(z=\frac{171}{7}\approx24.4\) (rounded to the nearest tenth).

Answer:

\(24.4\)