Question

what is the value of w?
31°
13w+30°
w+39°
write your answer as an integer or as a decimal rounded to the nearest tenth.
w =
submit

Explanation:

Step1: Use exterior angle theorem

The exterior angle of a triangle equals the sum of the two non-adjacent interior angles. So:
$$13w + 30 = (w + 39) + 31$$

Step2: Simplify right-hand side

Combine the constant terms:
$$13w + 30 = w + 70$$

Step3: Isolate w terms

Subtract $w$ from both sides:
$$12w + 30 = 70$$

Step4: Isolate constant terms

Subtract 30 from both sides:
$$12w = 40$$

Step5: Solve for w

Divide both sides by 12:
$$w = \frac{40}{12} = \frac{10}{3} \approx 3.3$$

Answer:

$w \approx 3.3$