Please help me. Thank you.

33) BD = 5.36

34) x = 67

* Don't forget to put a degree sign with 34)

Step-by-step explanation:

33)

In this problem, it is given that 2 of the sides are congruent, this means that the given triangle, by definition is isosceles. Yet if one adds up the given angle measures;

m< BAC = m<BAD + m<DAE + m<EAC -> Parts whole postulate

m<BAC = 15 + 30 + 15

m<BAC = 60

An isosceles triangle with a 60 angle is an equilateral triangle, therefore, one can say that all the sides and angles are congruent.

BA = AC -> sides equliateral triangle

m<B = m<C -> angles in an equilateral triangle

m<BAD = m<EAC -> given

ΔBAD ≅ ΔEAC -> side-angle-side

Therefore one can say that;

BD = EC ->corresponding parts of congruent triangles are congruent

Hence;

BD + DE + EC = BC

2BD + 9.28 = 20

2BD = 10.72

BD = 5.36

34)

1) m<PQL = y -> naming

2) m<PQL = m<LQN -> definiton of angle bisector

3) m<PQL + m<QLP + m<LPQ = 180 -> sum angles in a triangle

y + 70 + x = 180

x = 110 - y

4) m<PQL + m<LQM = 2y = m<PQM -> parts-whole-postulate

5) m<QLM = 180 - m<LQN + m<M -> sum of angles in a triangle

m<QLM = 126 - y

6) m<QLM + m<PLQ + m<NLP = 180 -> definition of a straight angle

126 + 70 + m<NLP = 180

m<NLP = y - 16

7) ΔPNL - isosceles -> deinfion of isosceles; Pn = NL

8) m<NPL + m<QPL = m<P -> parts-whole posulate

9) m<PQM + m<P = 180 -> two parralell lines intersected by a transversal

(110 - y) + (y - 16) + 2y = 180

94 + 2y = 180

2y = 86

y = 43

10) 110 - y = x -> substitution

110 - 43 = x

67 = x