Question

what is the value of w? write your answer as an integer or as a decimal rounded to the nearest tenth. w =

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, $2w + 38=(13w - 9)+37$.

Step2: Simplify the right - hand side

$(13w - 9)+37=13w+(-9 + 37)=13w + 28$. So the equation becomes $2w+38 = 13w+28$.

Step3: Isolate the variable terms

Subtract $2w$ from both sides: $2w - 2w+38=13w - 2w+28$, which simplifies to $38 = 11w+28$.

Step4: Solve for $w$

Subtract 28 from both sides: $38 - 28=11w+28 - 28$, so $10 = 11w$. Then divide both sides by 11: $w=\frac{10}{11}\approx0.9$.

Answer:

$0.9$