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 exterior - angle property

The exterior - angle of a triangle is equal to the sum of the two non - adjacent interior angles. So, $(2a + 43)+(18a-46)=22a - 17$.

Step2: Simplify the left - hand side

Combine like terms: $(2a+18a)+(43 - 46)=20a - 3$.
So, the equation becomes $20a-3 = 22a-17$.

Step3: Solve for a

Subtract $20a$ from both sides: $20a-20a - 3=22a-20a - 17$.
This gives $-3 = 2a-17$.
Add 17 to both sides: $-3 + 17=2a-17 + 17$.
We get $14 = 2a$.
Divide both sides by 2: $\frac{14}{2}=\frac{2a}{2}$.
So, $a = 7$.

Answer:

$a = 7$