Find the value of X:

Step-by-step explanation:

If AS is an angle bisector, then angle XAS is congruent to angle PAS; mathematically, that looks like this:

3x + 15 = 2x + 30 and x = 15.

3(15) + 15 = angle XAP, which is 120.

Because angle XAS is congruent to angle PAS, then the sides across from those congruent angles also should be congruent. Let's check it, just to make sure:

XS = PS --> 2(15) + 9 = 39 and 4(15) - 21 = 39. So that checks out. Because AS is congruent to itself by the reflexive property, then what this means is that triangle XAS is congruent to triangle PAS, making angle x and P the same measure. Looking at the whole big triangle, triangle XAP, if angle XAP measures 120, then angle X = angle P = (180 - 120) / 2, so angle X = 30.

divide by 5

step-by-step explanation:

60/5 = 12

d. bc = 12 and ef = 16

step-by-step explanation:

we are given that δabc : δdef such that .

also, it is given that

so, from the options, we need that .

a.

b.

c.  

d.

as, we can see that only option d gives the same ratio as i.e. .

hence, the possible lengths are bc = 12 and ef = 16.