Can someone me with this. i’m having difficulty on this.

  1a. HL; rotation

  1b. AAS; rotation

  2. 45°

  3. ∠1=57°; ∠2=75°; ∠3=44°

  4. x=5; y=8; z=11

Step-by-step explanation:

1a. The horizontal line is a leg of each right triangle. The hypotenuse of each right triangle is marked congruent, so the two right triangles are congruent by the HL theorem. The bottom triangle is rotated 180° from the top one (about the midpoint of the horizontal segment).

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1b. The vertical angles are congruent, as are the right angles. The marked sides are congruent, but are not between the congruent angles, so the AAS postulate applies. Again, the bottom triangle is 180° rotated from the top one (about their common vertex).

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2. Exterior angle D is the sum of remote interior angles B and C, so ...

  105° = 60° + ∠B

  45° = ∠B

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3. ∠1 is supplementary to 123°, so is 180°-123° = 57°.

∠2 is a remote interior angle with respect to exterior angle 123°, so it plus 48° will total 123°. 123° -48° = 75° = ∠2

∠3 is the third angle in a triangle whose other two angles are 123° and 13°, so its measure is ...

  180° -123° -13° = 44° = ∠3

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4. The triangles are congruent, so corresponding sides and angles are the same measure.

  4x +4 = 24  ⇒  x = (24/4) -1 = 5

  22 -y = 14  ⇒  y = 22 -14 = 8

  (3z)° +128° +19° = 180°  ⇒  z = (180 -147)/3 = 11

the answers are in the picture below

Step-by-step explanation:

we know that

applying the law of sines

°

so

∠j=18°

∠k=29°

∠l=180-(18+29)=133°

the answer part a) is

the measure of angle k is  ≈29°

part b)  the measure of angle k could also be

(180-29)=151°

so

∠j=18°

∠k=151°

∠l=180-(18+151)=11°

the answer part b) is

the measure of angle k could also be 151°

read more on -

there has been genes found in the x chromosome of males that have been linked to [homo/hetero]sexuality. in addition to the reign of the x chromosome, a section of chromosome 8 has also been link to, "alot of ppl are so " these facts were proven true after a 2014 study of a gay male and his strait brother. according to newscientist.com,"chromosome 14 and is mainly active in the thyroid, but also the brain. called tshr, it makes a type of receptor protein that recognises and binds to a hormone that stimulates the thyroid. in this way, the gene plays an important role in controlling thyroid function. the fact that tshr seems to be involved in sexual orientation fits with evidence that thyroid function seems to be linked to sexuality."

in conclusion, "ppl are so gay" due to their genetics.