Question

Given: AO = OD
OB = OC
m∠1=74˚, m∠2=36˚
Find: m∠ACD

Answer 1

First of all m<1 + m<2 = m<ACD

Soo we just need to add them.

74 + 36 = 110

So m<ACD = 110 degrees.

GOOD LUCK! :)

Answer 2

`m\angle ACD=110^(\circ)`

Explanation:

Given information: AO = OD, OB = OC, m∠1=74˚, m∠2=36˚.

In triangle OAB and ODC,

`AO=OD` (Given)

`m\angle AOB=m\angle DOC` (Vertical angles)

`OB=OC` (Given)

By SAS postulate,

`\triangle OAB\cong \triangle ODC`

`\angle OBA\cong \triangle OCD` (CPCTC)

`m\angle OBA=m\triangle OCD`

`74^(\circ)=m\triangle OCD`

From the given figure it is clear that

`\angle ACD=\angle ACO+\angle OCD`

`\angle ACD=36^(\circ)+74^(\circ)`

`\angle ACD=110^(\circ)`

Therefore, the measure of angle ACD is 110°.