Question

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

Explanation:

Step1: Recall exterior - angle property

The exterior - angle of a triangle is equal to the sum of the two non - adjacent interior angles.
So, \(10w + 12=(w + 30)+45\).

Step2: Simplify the right - hand side

\(10w+12=w + 75\).

Step3: Isolate the variable terms

Subtract \(w\) from both sides: \(10w - w+12=w - w + 75\), which gives \(9w+12 = 75\).

Step4: Isolate the variable

Subtract 12 from both sides: \(9w+12 - 12=75 - 12\), so \(9w=63\).

Step5: Solve for \(w\)

Divide both sides by 9: \(w=\frac{63}{9}=7\).

Answer:

7