Answer:
Part 1) [tex]x=10\ units[/tex]
Part 2) [tex]y=4.5\ units[/tex]
Part 3) [tex]z=7.5\ units[/tex]
Part 4) [tex]m<j=140\°[/tex]
Part 5) [tex]m<k=72\°[/tex]
Step-by-step explanation:
we know that
If two figures are similar, then the ratio of its corresponding sides is equal and its corresponding angles are congruent
so
[tex]\frac{y}{3}=\frac{6}{4}=\frac{z}{5}=\frac{15}{x}[/tex]
step 1
Find the measure of x
[tex]\frac{6}{4}=\frac{15}{x}[/tex]
[tex]x=4*15/6=10\ units[/tex]
step 2
Find the measure of y
[tex]\frac{y}{3}=\frac{6}{4}[/tex]
[tex]y=3*6/4=4.5\ units[/tex]
step 3
Find the measure of z
[tex]\frac{6}{4}=\frac{z}{5}[/tex]
[tex]z=5*6/4=7.5\ units[/tex]
step 4
Find the measure of angle j
we know that
The corresponding angles are congruent
In this part
[tex]m<j+40\°=180\°[/tex] -----> by consecutive interior angles (supplementary angles)
so
[tex]m<j=180\°-40\°=140\°[/tex]
step 5
Find the measure of angle k
we know that
[tex]m<k=72\°[/tex] ------> by corresponding angles
