Question

Can someone help me with numbers 10,11,12 plzzz show work I need help plzzzz

Answer 1

Answer:

  10. JL = 4

  11. m∠KML = 45°

  12. see below for a full list of angle measures; x = 30

Step-by-step explanation:

10. In the square, the diagonals are both the same length, and point N is their midpoint. That means ...

  KM = 2·JN

  4z -8 = 2(4z -10) . . . . substitute the given expressions

  4z -8 = 8z -20 . . . . . .eliminate parentheses

  12 = 4z . . . . . . . . . . . .add 20-4z to both sides

  KM = 12 -8 = 4 . . . . . substitute for 4z in the expression for KM

  JL = KM = 4

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11. All the sides and angles that look like they're the same measure are the same measure. Any angle not 90° is 45°. m∠KML = 45°

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12. For this, you make use of the properties of a rhombus. The diagonals of a rhombus are perpendicular bisectors of each other, so all of the angles where the diagonals meet are 90°.

Then within each triangle, the angles not 50° are their complement, 40°.

Angles in opposite corners are congruent to each other, and each diagonal bisects the corner angle. So ...

  ∠GHJ = ∠GKJ = 100°

  ∠GHK = ∠JHK = ∠GKH = ∠JKH = 50°

  ∠HGK = ∠HJK = 80°

  ∠HJG = ∠KJG = ∠KGJ = ∠KJG = 40°

We have already said the central angle is 90°, so ...

  (5x -60)° = 90°

  x -12 = 18 . . . . . . divide by 5°

  x = 30 . . . . . . . . add 12