Question

what is the value of w? w - 42° w - 34° w + 36°

Explanation:

Step1: Apply exterior - angle theorem

The exterior - angle of a triangle is equal to the sum of the two non - adjacent interior angles. So, $(w + 36^{\circ})=(w - 42^{\circ})+(w - 34^{\circ})$.

Step2: Simplify the right - hand side

$(w + 36^{\circ})=w - 42^{\circ}+w - 34^{\circ}$. Combine like terms: $w + 36^{\circ}=2w-76^{\circ}$.

Step3: Solve for w

Subtract w from both sides: $36^{\circ}=2w - w-76^{\circ}$. Then $36^{\circ}=w - 76^{\circ}$. Add $76^{\circ}$ to both sides: $w=36^{\circ}+76^{\circ}=112^{\circ}$.

Answer:

$112^{\circ}$