Question

I’d appreciate if someone could help me out lol

Answer 1

a) OP:RT = 10:3

b) OQ = 15 cm

c) m<P =
`60^(o)`

d) m<Q =
`94^(o)`

Explanation:

Given that: ΔOPQ is similar to ΔRTS

Then;

a) OP:RT = 12:3.6

=
`(120)/(36)`

=
`(10)/(3)`

= 10:3

The ratio of OP to RT is 10:3.

b) The measure of length OQ =
`(10)/(3)` x 4.5

= 15 cm

c) m<P ≅ m<T

So that,

m<P =
`60^(o)`

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)

=
`94^(o)`

Thus,

m<Q =
`94^(o)`