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, $a + 100=(20a-78)+(a + 53)$.

Step2: Simplify the right - hand side

$(20a-78)+(a + 53)=20a+a-78 + 53=21a-25$. So the equation becomes $a + 100=21a-25$.

Step3: Isolate the variable terms

Subtract $a$ from both sides: $100=21a-a-25$, which simplifies to $100 = 20a-25$.

Step4: Solve for $a$

Add 25 to both sides: $100 + 25=20a$, so $125 = 20a$. Then divide both sides by 20: $a=\frac{125}{20}=6.25$.

Answer:

$6.25$