Question

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

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, $(43a + 58)=(89a-79)+51$.

Step2: Simplify the equation

First, expand the right - hand side: $43a + 58=89a-79 + 51$. Combine like terms on the right - hand side: $43a+58=89a - 28$.

Step3: Move terms with 'a' to one side

Subtract $43a$ from both sides: $58=89a-43a - 28$. This gives $58 = 46a-28$.

Step4: Isolate 'a'

Add 28 to both sides: $58 + 28=46a$, so $86 = 46a$. Then divide both sides by 46: $a=\frac{86}{46}\approx1.9$.

Answer:

$1.9$