Question

a triangle has interior angle measures of 2z, 2z + 8°, and 2z + 3°. what is the value of z?
write your answer as an integer or as a decimal rounded to the nearest tenth.
z = □°

Explanation:

Step1: Use the triangle angle - sum property

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \(2z+(2z + 8)+(2z+3)=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(2z+2z + 8+2z+3=(2z+2z+2z)+(8 + 3)=6z+11\).
The equation becomes \(6z+11 = 180\).

Step3: Solve for \(z\)

Subtract 11 from both sides: \(6z=180 - 11=169\).
Then divide both sides by 6: \(z=\frac{169}{6}\approx28.2\).

Answer:

\(28.2\)