Question

what is the value of y? y - 30° y + 43° y - 33° y =

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, $y + 43^{\circ}=(y - 30^{\circ})+(y - 33^{\circ})$.

Step2: Simplify the right - hand side

$(y - 30^{\circ})+(y - 33^{\circ})=y+y-(30^{\circ}+33^{\circ})=2y - 63^{\circ}$. So the equation becomes $y + 43^{\circ}=2y-63^{\circ}$.

Step3: Solve for y

Subtract y from both sides: $y - y+43^{\circ}=2y - y-63^{\circ}$. This gives $43^{\circ}=y - 63^{\circ}$. Then add 63^{\circ} to both sides: $43^{\circ}+63^{\circ}=y-63^{\circ}+63^{\circ}$. So $y = 106^{\circ}$.

Answer:

$106$