Answer:
1. B. ∠2 and ∠6
2. 50°
3. Option 1, Option 5, and Option 6.
4. 133°
Work for question 4:
180°-47° = 133°
Explanation:
1.
Alternate means the angles are on different sides of the transversal (horizontal line in this case). Interior means they are between the parallel lines (lines a and b in this case). (∠2 and ∠6) and (∠3 and ∠7) are the alternate interior angles but only the first is an option.
2.
∠10 = ∠8+∠7 (corresponding angles so they are congruent)
∠10 is 140° and ∠8 is a right angle
140-90 = 50
∠7 = 50°
∠4 = 50° (∠7 and ∠4 are vertical angles so they are congruent)
3.
Sense all angles of a triangle add up to 180 and the ratio of angles is 3:3:6 the we can find the angle with the equation x+x+2x=180
Simplify.
4x=180
Solve by dividing 4 from both sides
x=45
so it is a 45, 45, 90 triangle. (right triangle because the 90 and icoceles because other 2 angles are congruent so option 5 is correct)
m∠J= 45°
m∠K= 45° (Option 1 is correct)
m∠L= 90° (Option 6 is correct)
4.
I honestly don't see how you can solve this without making assumptions so I will make assumptions.
Assuming the whole figure is symmetrical vertically ∠1 is congruent to the same spot on the right side of the shape. This angle would be supplementary to the angle of the angle outside of the shape adjacent on the right making the angle (which is corresponding, therefore congruent to ∠2) 133°.