Question

determine all the marked angles in the following figure in which l || m.

Explanation:

Step1: Use corresponding - angle property

Since l || m, the angle corresponding to the 50 - degree angle is also 50 degrees. Let's call this angle a.

Step2: Use angle - sum property of a triangle

In the triangle formed, we know one angle is a = 50 degrees and another is 60 degrees. Let the third angle be b. By the angle - sum property of a triangle (the sum of interior angles of a triangle is 180 degrees), we have b=180-(50 + 60).
b = 180-110=70 degrees.

Step3: Use linear - pair property

The angle adjacent to b forms a linear pair with b. Let this angle be c. Since the sum of angles in a linear pair is 180 degrees, c = 180 - 70=110 degrees.

Answer:

The marked angles are 50 degrees, 60 degrees, 70 degrees, 110 degrees.