Question

1. find the measure of ∠j.

Explanation:

Step1: Identify vertical - angles

Vertical angles are equal. The angle opposite the 50 - degree angle has a measure of 50 degrees.

Step2: Use angle - sum property of a triangle

The sum of angles in a triangle formed by the intersection of lines is 180 degrees. Let's assume the triangle formed where angle \(j\) is located. One angle of the triangle is 50 degrees and another is 65 degrees.
We know that for a triangle with angles \(A\), \(B\), and \(C\), \(A + B+C=180^{\circ}\). Let \(A = 50^{\circ}\), \(B = 65^{\circ}\), and \(C = j\). Then \(j=180-(50 + 65)\).

Step3: Calculate the value of \(j\)

$$j=180-(50 + 65)=180 - 115=65^{\circ}$$

Answer:

\(65^{\circ}\)