Question

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

Explanation:

Step1: Apply exterior - angle theorem

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

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

Step3: Solve for a

Subtract $10a$ from both sides: $52=3a + 26$. Then subtract 26 from both sides: $3a=52 - 26=26$. Divide both sides by 3: $a=\frac{26}{3}\approx8.67$.

Answer:

$a\approx8.67$