Answer:
33) BD = 5.36
34) x = 67
* Don't forget to put a degree sign with 34)
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