Question

For what value of x is line m parallel to line n?

Answer 1

If m and n are parallel then x = 20.

Explanation:

In order to find this, we must note that the 65 degree angle and the 3x + 5 degree angle would be congruent. Therefore, we can set the m equal to each other and solve for x.

3x + 5 = 65

3x = 60

x = 20

Answer 2

At 20 value of x, line m is parallel to line n.

According the given diagram, line m and n are parallel to each other. We know, in parallel lines, alternate angles, vertically opposite angles, corresponding angles are equal to each other.

To find the value of x, we need to find any of the above mentioned angles in reference of x.

As seen in the diagram, it can be said that angle 65 degree and angle 3x+5 are corresponding to each other.

In geometry, corresponding angles are pairs of angles that are in the same relative position at each intersection where a straight line meets another line. Specifically, corresponding angles are formed when a transversal intersects two parallel lines.

So, by the property of corresponding angles, we can equate both angles:

3x + 5 = 65

=> 3x = 65 - 5

=> 3x = 60

=> x = 60/3

=> x = 20

Question: