Question

what is the value of z?
triangle with angles: 18z, 37°, and exterior angle 26z+9°
write your answer as an integer or as a decimal rounded to the nearest tenth.
z = °

Explanation:

Step1: Use exterior angle theorem

The exterior angle theorem states that an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. So, we have the equation $26z + 9=18z + 37$.

Step2: Solve for z

Subtract $18z$ from both sides of the equation:
$26z-18z + 9=18z-18z + 37$
$8z+9 = 37$
Subtract 9 from both sides:
$8z+9 - 9=37 - 9$
$8z=28$
Divide both sides by 8:
$z=\frac{28}{8}=3.5$

Answer:

$3.5$