Question

what is the value of a? 10a + 52° 12a a + 26° write your answer as an integer or as a decimal round a =

Explanation:

Step1: Apply exterior - angle property

The exterior - angle of a triangle is equal to the sum of the two non - adjacent interior angles. So, $10a + 52=(a + 26)+12a$.

Step2: Simplify the equation

Combine like terms: $10a+52=a + 26+12a$.
$10a+52 = 13a+26$.

Step3: Isolate the variable

Subtract $10a$ from both sides: $52=13a - 10a+26$.
$52 = 3a+26$.
Then subtract 26 from both sides: $3a=52 - 26$.
$3a = 26$.

Step4: Solve for a

Divide both sides by 3: $a=\frac{26}{3}\approx8.67$.

Answer:

$a=\frac{26}{3}\approx8.67$