Question

Picture below, 100 points for a correct answer

Answer 1

53

Explanation:

connect the two points and you will notice that the inside angles form opposite angles across the parallel lines that will add up to 180

therefore the inside angles that are part of the newly formed triangle must sum to

148+159-180 = 127

then since the angles in a triangle add to 180,

180 - 127 = 53

hope this helps

Answer 2

n = 53°

Explanation:

The transversal line connecting the vertex of angle 148° to the vertex of angle 159° intersects two parallel lines and creates a triangle to its left (see attached diagram).

According to the Consecutive Interior Angles Theorem, when two parallel lines are intersected by a transversal, the angles that are interior to the parallel lines and on the same side of the transversal line are supplementary (sum to 180°).

Therefore, the sum of the purple and blue interior angles of the triangle are equal to the sum of angle 148° and angle 159° less 180°.

Since the interior angles of a triangle sum to 180°, then:

n = 180° - (148° + 159° - 180°)

Solve for n:

n = 180° - (307° - 180°)

n = 180° - (127°)

n = 53°

So, the size of angle n in the provided diagram is 53°.