I need help
a)104
b)128
c)120
d)74
e)87

m∠JTS = 104° ⇒ (A)

Step-by-step explanation:

The measure of an exterior angle of a triangle at one of its vertices equals the sum of the measures of the opposite interior angles.

Let us use this fact to solve the question

In ΔTSR

∵ T ∈ ray RJ

∴ ∠JTS is an exterior angle of ΔTSR

→ By using the fact above

∴ ∠TSR and ∠TRS are the opposite interior angles to ∠JTS

∴ m∠JTS = m∠TSR + m∠TRS

∵ m∠JTS = 27x - 4

∵ m∠ TSR = 30°

∵ m∠TRS = 18x + 2

→ Substitute their values in the equation above

∴ 27x - 4 = 30 + 18x + 2

→ Add the like terms in the right side

∴ 27x - 4 = 18x + 32

→ Add 4 to both sides

∴ 27x = 18x + 36

→ Subtract 18x from both sides

∴ 9x = 36

→ Divide both sides by 9

∴ x = 4

→ To find m∠JTS substitute x by 4 in its measure

∴ m∠JTS = 27(4) - 4 = 108 - 4

∴ m∠JTS = 104°

the answer is; biodiversity resulting from few ancestors

adaptive radiation occurs when a population is subjected to a large natural environment with spatial ecological variations. the parts of the population in the different ecologies begin to adapt to their local environments. due to non-random mating across the large populations, this causes the different populations from the large population to speciate within their local environments. they, therefore, diverge to different species sharing a common ancestor.  

geometry: triangles

solvers

lessons

answers archive

call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

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