Question

what is the value of y? 114° a. 33° b. 57° c. 66° d. 114°

Explanation:

Step1: Find the interior - angle adjacent to 114°

The interior - angle adjacent to 114° and 114° are supplementary. Let the interior - angle be $x$. Then $x + 114^{\circ}=180^{\circ}$, so $x = 180^{\circ}-114^{\circ}=66^{\circ}$.

Step2: Use the angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. In the triangle, we have two equal angles $y$ and the third angle $x = 66^{\circ}$. So $y + y+66^{\circ}=180^{\circ}$, which simplifies to $2y=180^{\circ}-66^{\circ}=114^{\circ}$.

Step3: Solve for $y$

Dividing both sides of $2y = 114^{\circ}$ by 2, we get $y=\frac{114^{\circ}}{2}=57^{\circ}$.

Answer:

B. $57^{\circ}$