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 = 28

Explanation:

Step1: Sum angles to 180°

$$(2w-17^\circ) + 38^\circ + (4w-10^\circ) = 180^\circ$$

Step2: Simplify left side

$$6w + 11^\circ = 180^\circ$$

Step3: Isolate term with $w$

$$6w = 180^\circ - 11^\circ = 169^\circ$$

Step4: Solve for $w$

$$w = \frac{169^\circ}{6}$$

Answer:

$28.2$ (rounded to the nearest tenth)