Question

w+3° w+34° y w y = \boxed{ } ° submit

Explanation:

Step1: Use exterior angle theorem

The exterior angle theorem states that an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. So, \(w + 34=(w + 3)+w\)

Step2: Solve for \(w\)

Simplify the right - hand side of the equation: \(w + 34=2w+3\)
Subtract \(w\) from both sides: \(34 = w + 3\)
Subtract 3 from both sides: \(w=34 - 3=31\)

Step3: Find \(y\)

Since \(y\) and \(w + 34\) are supplementary (they form a linear pair), \(y=180-(w + 34)\)
Substitute \(w = 31\) into the equation: \(y=180-(31 + 34)=180 - 65 = 115\)
Or we can also use the fact that the sum of interior angles of a triangle is \(180^{\circ}\). The two non - adjacent interior angles to the exterior angle \(w + 34\) are \(w\) and \(w + 3\), and \(y\) is adjacent to the exterior angle. Also, in the triangle, the sum of angles: \(y+(w + 3)+w=180\). We know \(w = 31\), so \(y+(31 + 3)+31=180\), \(y+65 = 180\), \(y = 115\)

Answer:

\(115\)