Question

1. error analysis gary determined that the value of x is 103 and the value of y is 137 in the figure below. what mistake did gary make?

Explanation:

Step1: Find the third - angle of the triangle

The sum of interior angles of a triangle is 180°. Let the third - angle of the triangle be $z$. So, $z=180-(48 + 77)=180 - 125 = 55^{\circ}$.

Step2: Use the property of vertical angles

The angle $y$ and the 55° angle in the triangle are vertical angles. Vertical angles are equal. So, $y = 55$.

Step3: Use the property of linear - pair

The angle $x$ and the 55° angle (adjacent to it) form a linear - pair. A linear - pair of angles sums to 180°. So, $x=180 - 55=125$.

Answer:

The value of $x$ is 125 and the value of $y$ is 55.