Answer/Step-by-step explanation:
Given:
m<A = 29°
PA = 13 cm
LN = 21 cm
Since ∆ACP ≅ ∆LNX (isosceles ∆s), therefore,
<A = <L
<C = <N
<P = <X
AC = LN
XL = PA
XN = PC
since, XL = XN (equal sides of isosceles ∆LNX), therefore, PA = PC
Thus,
Since XL = PA
XL = 13 cm (substitution)
Since AC = LN
AC = 21 cm (substitution)
Since PC = PA,
PC = 13 cm (substitution)
Since <L = <A,
m<L = 29° (substitution)
Since ∆ACP is an isosceles ∆, the base angles are equal. Therefore,
m<C = m<A
m<C = 29° (substitution)
m<X = m<P
m<P = 180 - (29 + 29) (sum of ∆ACP)
m<P = 122°
Therefore,
m<X = 122° (corresponding angles of congruent ∆s)
