Question

In rectangle FGHL, HL = 12 feet, GH = 8 feet, GL = 14 feet, and m∠LHF = 30°.

Answer 1

A. m∠FHG
B. m∠HFG
C. m∠FJG
D. m∠GLF
E. HJ
F. GF

Answer 2

Remember that opposite sides of a rectangle are equal to each other, and that if two angles make a right angle, then they add up to 90 degrees (complementary).

Answer 3

One angle is already done. which is 30 degrees. Wouldn't A through B all equal to 30 degrees since they're flipped?

Answer 4

Also remember that when you see a Z between 2 parallel lines and one transversal, the alternate interior angles are equal

Answer 5

You're right, B would also be 30. However, to find A you'd need to do 90 minus 30

Answer 6

Ok, so 60. How would I go about figuring the rest.

Answer 7

Since they're different

Answer 8

Hmm. You could find F easily, since it's the same length as one of the ones given to you

Answer 9

Would FJG be 90 degrees?

Answer 10

or 120?

Answer 11

Ok, how am I suppose to read this? J is the center. And I'm trying to figure out FJG. F and G would be 30 correct?

Answer 12

Well, it probably won't be 120 degrees, since the sum of a triangle's angles is 180, and one angle we know is already 60.

Answer 13

Got it. Because a rectangle's diagonals bisect each other, the triangles are isosceles, so 2 angles of the triangles are congruent, as well as 2 sides. Try using that to find the rest.

Answer 14

Angle GFJ would be 60, so angle JGF would also be 60. Now try finding the other angle in that triangle.

Answer 15

Do 180 minus the sum of the 2 angles to find the third angle for each triangle, and remember that, since 14 is the length of one diagonal, and since the diagonals bisect each other, one part of the diagonal would be half of 14. Also, the diagonals of a rectangle are congruent (equal).

Answer 16

Also, use pythagorean theorem if you need to

Answer 17

So, D would equal to 90 degrees then since I would subtract 90 degrees from 180?

Answer 18

No, D would be 30, since the triangles are isosceles. Sorry for the late response

Answer 19

Thanks for the medal and testimonial :D