Answer:
A. ΔJKL and ΔLMN have only one pair of angles that are congruent
C. ΔJKL has angles that measure [tex]50^o,60^o,70^o[/tex]
Step-by-step explanation:
step 1
Find the value of x
we know that
[tex]m\angle KLJ=m\angle MLN[/tex] ----> by vertical angles
substitute the given values
[tex](6x-2)^o=(5x+10)^o[/tex]
solve for x
[tex]6x-5x=10+2\\x=12[/tex]
step 2
Find the measure of the interior angles of triangle JKL
we have
[tex]m\angle KLJ=(6(12)-2)=70^o[/tex]
[tex]m\angle KJL=(5(12))=60^o[/tex]
Remember that the sum of the interior angles in any triangle must be equal to 180 degrees
so
[tex]m\angle JKL=180^o-130^o=50^o[/tex]
therefore
Triangle JKL has angles that measure [tex]50^o,60^o,70^o[/tex]
step 3
Find the measure of the interior angles of triangle LMN
we have
[tex]m\angle MLN=(5(12)+10)=70^o[/tex]
[tex]m\angle LMN=(6(12)-7)=65^o[/tex]
Remember that the sum of the interior angles in any triangle must be equal to 180 degrees
so
[tex]m\angle LNM=180^o-135^o=45^o[/tex]
Triangle LMN has angles that measure [tex]45^o,65^o,70^o[/tex]
we know that
If two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent
The corresponding angles of triangle JKL and LMN are not congruent
therefore
The triangles are not similar
Verify each statement
Part a) ΔJKL and ΔLMN have only one pair of angles that are congruent
The statement is true (see the explanation)
Part b) ΔJKL and ΔLMN have two pairs of angles that are congruent
The statement is false
Because have only one pair of angles that are congruent
Part c) ΔJKL has angles that measure [tex]50^o,60^o,70^o[/tex]
The statement is true (see the explanation)
Part d) ΔLMN has angles that measure [tex]50^o,60^o,70^o[/tex]
The statement is false
Because, Triangle LMN has angles that measure [tex]45^o,65^o,70^o[/tex]
Part e) ΔJKL and ΔLMN are similar
The statement is false
Because, the corresponding angles are not congruent
