Question

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

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, \(7a - 6=(6a - 49)+3a\).

Step2: Simplify the equation

First, simplify the right - hand side of the equation: \((6a - 49)+3a=6a + 3a-49=9a - 49\). Then the equation becomes \(7a - 6=9a - 49\).

Step3: Solve for \(a\)

Subtract \(7a\) from both sides: \(-6 = 9a-7a - 49\), which simplifies to \(-6 = 2a-49\). Then add \(49\) to both sides: \(2a=-6 + 49\), so \(2a = 43\). Divide both sides by \(2\): \(a=\frac{43}{2}=21.5\).

Answer:

\(21.5\)