Question

the diagram shows a triangle. what is the value of a? a =

Explanation:

Step1: Recall angle - sum property

The sum of interior angles of a triangle is 180°. So, $(a + 9)+(2a+19)+(3a - 10)=180$.

Step2: Combine like - terms

Combine the terms with 'a' and the constant terms: $(a+2a + 3a)+(9 + 19-10)=180$. This simplifies to $6a+18 = 180$.

Step3: Isolate the variable term

Subtract 18 from both sides of the equation: $6a=180 - 18$, so $6a=162$.

Step4: Solve for 'a'

Divide both sides by 6: $a=\frac{162}{6}=27$.

Answer:

$27$