Question

Help please?

Answer 1

`color(blue)("a " 30^@, "b " 60^@, "c " 30^@, " d " 90^@, "e " 90^@, "f " 270^@, "g " 120^@)`

Explanation:

`/_SOR+/_SOA=180^@` Supplementary.

`/_SOA=30^@`

a) `30^@`

`/_OSA=180^@-(/_SOA+90^@)=60^@` Angles in triangle `DeltaSOT`

b) `60^@`

`Delta OSM` is isosceles, so:

`/_SOA=/_AMO=30^@`

c) `30^@`

`/_SOM=180^@-(/_OSA+/_AMO)=90^@` Angles in `Delta SOM`

d) `90^@`

`/_SOM=90^@`, so `mhat(SM)=90^@`

e) `90^@`

`/_MOA=180^@-(/_AOM+/_AMO)=60^@`

`/_SOM+/_SOR+/_ROM=360^@`

`/_SOR+/_ROM=360^@-/_SOM=270^@`, so:

`mhat(SRM)=/_SOR+/_ROM=270^@`

f) `270^@`

`/_ROM=120^@`, so:

`mhat(RM)=120^@`

g) `120^@`

`color(blue)("a " 30^@, "b " 60^@, "c " 30^@, " d " 90^@, "e " 90^@, "f " 270^@, "g " 120^@)`