Question

CAN SOMEONE PLEASE HELP ME? THANK YOU

Answer 1

`m\angle6 = \boxed{\bold{140}}^(\circ)`

Explanation:

When two parallel lines intersect the following relationships amongst the angles hold

Corresponding angles: These are angles that are in the same position relative to the parallel lines, but on different lines. Corresponding angles are congruent. Here the pairs of corresponding angles are:

∠1 and ∠3: m∠1 = m∠3
∠2 and ∠4: m∠2 = m∠4
∠8 and ∠6 m∠8 = m∠6
∠7 and ∠5: m∠7 = m∠5

Same-side interior angles: These are angles that are inside the parallel lines, on the same side of the transversal. Same-side interior angles are supplementary, which means their measures add up to 180 degrees

∠1 and ∠8 are supplementary angles.
So m∠1 + m∠8 = 180°
Since m∠1 = 40°
m∠8 = 180° - 40° = 140°

Since ∠8 and ∠6 are corresponding angles, and m∠8 = m∠6

we have 140° = m∠6

So m∠6 = 140°

There are relationships among the other angles, just look them up

Answer 2

angle 6 = 140°

Explanation:

Since j and k are parallel, any line intersecting the two parallel lines will create a set of angles that are identical to each other.

Top Angles Bottom Angles

1 = 3

2 = 4

7 = 5

8 = 6

We also know that the sum of angles formed by an intersection of 2 lines is 360 degrees. Each side is 180 degrees.

This means that angles 1 + 8 = 180 degrees. If angle 1 is 40 degrees, angle 8 is 180 - 40 or 140 degrees.

From above, angles 8 and 6 are equal, so angle 6 = 140°