Question

the diagram shows a triangle.
what is the value of w?
write your answer as an integer or as a decimal rounded to the nearest tenth.
w = \\(\square\\)°

Explanation:

Step1: Sum of triangle angles

The sum of interior angles in a triangle is $180^\circ$. So we set up the equation:
$$2w + 3w + (w + 16^\circ) = 180^\circ$$

Step2: Combine like terms

Add the terms with $w$ together:
$$6w + 16^\circ = 180^\circ$$

Step3: Isolate the variable term

Subtract $16^\circ$ from both sides:
$$6w = 180^\circ - 16^\circ = 164^\circ$$

Step4: Solve for $w$

Divide both sides by 6:
$$w = \frac{164^\circ}{6} \approx 27.3^\circ$$

Answer:

$w \approx 27.3^\circ$