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: Apply exterior - angle theorem

The exterior - angle of a triangle is equal to the sum of the two non - adjacent interior angles. So, $a + 46=(2a - 11)+31$.

Step2: Simplify the right - hand side

$(2a - 11)+31=2a+(-11 + 31)=2a + 20$. So the equation becomes $a + 46=2a+20$.

Step3: Solve for a

Subtract a from both sides: $a+46 - a=2a + 20 - a$. This gives $46=a + 20$. Then subtract 20 from both sides: $46-20=a+20 - 20$. So, $a = 26$.

Answer:

$a = 26$