Question

Given the following diagram, if m ∠ COF = 150°, then m ∠ BOC = AD ⊥ BF

150 °
90 °
45 °
30 °

Answer 1

short answer: 30 degrees :)

Answer 2

`m\angle BOC=30^o`

Explanation:

step 1

Find the measure of angle COD

we know that

`m\angle COF=m\angle COD+m\angle DOF` ---> by addition angle postulate

we have

`m\angle COF=150^o` ----> given problem

`m\angle DOF=90^o` ----> because AD is perpendicular to BF

substitute the given values

`150^o=m\angle COD+90^o`

`m\angle COD=150^o-90^o`

`m\angle COD=60^o`

step 2

Find the measure of angle BOC

we know that

`m\angle BOC+m\angle COD=90^o` ---> by complementary angles

we have

`m\angle COD=60^o`

substitute

`m\angle BOC+60^o=90^o`

`m\angle BOC=90^o-60^o`

`m\angle BOC=30^o`