Determine the value of the α-and-β- angles shown in the below diagram:
Parallel Lines Geometry: Find α and β Using Given Angles 104° and 81°
Question
Video Solution
Solution Steps
00:00 Find the angles
00:03 Parallel lines according to the given
00:07 Alternate angles are equal between parallel lines
00:16 Corresponding angles are equal between parallel lines
00:24 And this is the solution to the question
Step-by-Step Solution
In the question, we can observe that there are two pairs of parallel lines, lines a and b.
When a line crosses two parallel lines, different angles are formed
Angles alpha and the given angle of 104 are on different sides of the transversal line, but both are in the interior region between the two parallel lines,
This means they are alternate angles, and alternate angles are equal.
Therefore,
Angle beta and the second given angle of 81 degrees are both on the same side of the transversal line, but each is in a different position relative to the parallel lines, one in the exterior region and one in the interior. Therefore, we can conclude that these are corresponding angles, and corresponding angles are equal.
Therefore,
Answer