Question

problem 15: (first taught in lesson 31) find x and y. after you enter your answer press go. x = y =

Explanation:

Step1: Use angle - sum property of a triangle

In the left - hand triangle, the sum of interior angles of a triangle is $180^{\circ}$. Let the third angle of the left - hand triangle be $z$. So, $z+50^{\circ}+75^{\circ}=180^{\circ}$, then $z = 180^{\circ}-(50^{\circ}+75^{\circ})=55^{\circ}$.

Step2: Find the value of $x$

The two parallel lines and the transversal form an angle relationship. The angle $x$ and the non - labeled angle in the left - hand triangle are alternate interior angles. Also, we can find $x$ using the fact that the exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. The exterior angle of the left - hand triangle at the bottom is $x + 75^{\circ}$. And the non - adjacent interior angles of the left - hand triangle are $50^{\circ}$ and the third angle $z = 55^{\circ}$. Another way is to note that the angle adjacent to $x$ and the $50^{\circ}+75^{\circ}$ angle in the triangle are supplementary. So $x=180^{\circ}-(50^{\circ}+75^{\circ}) - 80^{\circ}=25^{\circ}$.

Step3: Find the value of $y$

The angle $y$ and the $55^{\circ}$ angle in the triangle are supplementary (linear pair of angles formed by a straight line). So $y = 180^{\circ}-55^{\circ}=125^{\circ}$.

Answer:

$x = 25$, $y = 125$