Question

what is the value of a?
write your answer as an integer or as a decimal rounded to the nearest tenth.
a =

Explanation:

Step1: Use the 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, \(21a=8a+(18a - 27)\).

Step2: Simplify the equation

$$
LATEXBLOCK0
$$

Step3: Solve for \(a\)

Subtract \(21a\) from both sides: \(0 = 26a-21a - 27\), which simplifies to \(0 = 5a-27\). Then add \(27\) to both sides: \(5a=27\). Divide both sides by \(5\): \(a=\frac{27}{5}=5.4\).

Answer:

\(5.4\)