Question

what is the value of y? 15y - 51° 8y y + 22° write your answer as an integer or as a decimal rounded to the nearest tenth. 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, $15y - 51=(8y)+(y + 22)$.

Step2: Simplify the right - hand side

$(8y)+(y + 22)=8y+y + 22=9y + 22$. So the equation becomes $15y-51 = 9y+22$.

Step3: Move the terms with y to one side

Subtract $9y$ from both sides: $15y-9y-51=9y-9y + 22$, which simplifies to $6y-51 = 22$.

Step4: Move the constant to the other side

Add 51 to both sides: $6y-51 + 51=22+51$, so $6y=73$.

Step5: Solve for y

Divide both sides by 6: $y=\frac{73}{6}\approx12.2$.

Answer:

$y\approx12.2$