Question

question 3 of 10 what is the value of y? 130° y° y° a. 25° b. 50° c. 130° d. 65°

Explanation:

Step1: Find the interior - angle adjacent to 130°

The adjacent interior - angle and 130° are supplementary. Let this angle be $x$. Then $x + 130^{\circ}=180^{\circ}$, so $x = 180^{\circ}-130^{\circ}=50^{\circ}$.

Step2: Use the angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. In the triangle, the three angles are $x$, $y$, and $y$. So $x + y + y=180^{\circ}$. Substitute $x = 50^{\circ}$ into the equation: $50^{\circ}+2y = 180^{\circ}$.

Step3: Solve for $y$

First, subtract 50° from both sides of the equation: $2y=180^{\circ}-50^{\circ}=130^{\circ}$. Then divide both sides by 2: $y=\frac{130^{\circ}}{2}=65^{\circ}$.

Answer:

D. 65°