Question

Two parallel lines are cut by a transversal as shown below. Suppose m 2 = 59º. Find m5 and m 27. h 1 2 56 8 17

Answer 1

Angle 5 = 121º

Angle 7 = 121º

Step-by-step explanation

To answer this, we need to explain what Same side interior angles and vertically opposite angles are.

Same side interior angles occupy the interior side of where the transversal line crosses the two stright lines. If the two lines are parallel to each other, then the sum of same side interior angles is equal to 180 degrees.

Vertical angles (or vertically opposite angles) are angles that are directly opposite each other at a point where two straight lines intersect. Vertical angles are equal to each other.

From the diagram, we can see that Angle 2 is vertically opposite to Angle 4. Hence,

Angle 2 = Angle 4 = 59º (vertically opposite angles)

Then, we can see that Angle 4 and Angle 5 are same side interior angles. Hence,

Angle 4 + Angle 5 = 180º (Same side interior angles)

59º + Angle 5 = 180º

Angle 5 = 180º - 59º

Angle 5 = 121º

We can then further see that Angle 5 is vertically opposite to Angle 7. Hence,

Angle 5 = Angle 7 = 121º (vertically opposite angles)