Answer:
a) OP:RT = 10:3
b) OQ = 15 cm
c) m<P = [tex]60^{o}[/tex]
d) m<Q = [tex]94^{o}[/tex]
Step-by-step explanation:
Given that: ΔOPQ is similar to ΔRTS
Then;
a) OP:RT = 12:3.6
= [tex]\frac{120}{36}[/tex]
= [tex]\frac{10}{3}[/tex]
= 10:3
The ratio of OP to RT is 10:3.
b) The measure of length OQ = [tex]\frac{10}{3}[/tex] x 4.5
= 15 cm
c) m<P ≅ m<T
So that,
m<P = [tex]60^{o}[/tex]
d) m<Q ≅ m<S
But,
26 + 60 + m<S = 180 (sum of angles in a triangle)
86 + m<S = 180
m<S = 180 - (86)
= [tex]94^{o}[/tex]
Thus,
m<Q = [tex]94^{o}[/tex]
