Answer and Step-by-step explanation:
4. We are finding line AC.
AB is congruent to BC because the angles at the top are both 30 because of angle bisector. BD is congruent to BD, so triangles are congruent by SAS theorem. That means AB is congruent to BC by CPCTC (Congruent Parts of Congruent Triangles are Congruent).
With that being said, we can equal the expressions together.
-x + 25 = 3(2x - 8)
-x + 25 = 6x - 24
49 = 7x
7 = x
-(7) + 25 = 18
3(2(7) - 8) = 3(14 - 8) = 3(6) = 18
18 + 18 = 36
AC = 36
6. We are finding measure of angle UTW.
We have another angle bisector, so that side is equal to itself (TV ≅ TV)
We have UV and VW having the same length, so those are congruent.
Since this is a right triangle, these triangles are congruent by the HL (Hypotenuse-Leg) Theorem.
So, now we can equal the angles together.
2x + 3 = 5x - 24
27 = 3x
9 = x
2(9) + 3 = 18 + 3 = 21
5(9) - 24 = 45 - 24 = 21
21 + 21 = 42
m∠UTW = 42
#teamtrees #PAW (Plant And Water)
(Sorry for the late response, this took some time).