Question

what is the value of w?

Explanation:

Step1: Apply exterior - angle property

The exterior - angle of a triangle is equal to the sum of the two non - adjacent interior angles. So, $w + 48^{\circ}=(w + 2^{\circ})+(w + 14^{\circ})$.

Step2: Simplify the right - hand side

$(w + 2^{\circ})+(w + 14^{\circ})=w+w + 2^{\circ}+14^{\circ}=2w+16^{\circ}$. So the equation becomes $w + 48^{\circ}=2w+16^{\circ}$.

Step3: Solve for w

Subtract w from both sides: $48^{\circ}=2w - w+16^{\circ}$. Then $48^{\circ}=w + 16^{\circ}$. Subtract $16^{\circ}$ from both sides: $w=48^{\circ}-16^{\circ}=32^{\circ}$.

Answer:

$32$