Question

In this diagram, lines AB and CD are parallel. D B Angle ABC measures 35 degrees and angle BAC measures 115 degrees. a. What is m ZACD b. What is mZDCB c. What is mZACB

Answer 1

|CD| is parallel to |AB|

`\angle ACD=\angle ACB+\angle DCB`
`\begin{gathered} ACBisatriangle.Thesumofanglesinatriangleis180^o. \\ \angle ACB+\angle ABC+\angle BAC=180^o \\ \angle ACB=180^o-35^o-115^o \\ \angle ACB=30^o \end{gathered}`

Also;

`\begin{gathered} S\text{ ince CD and AB are parallel;} \\ \angle DCB=\angle ABC\text{ (because alternate angles are equal)} \\ \angle DCB=35^o \end{gathered}`
`\begin{gathered} \angle ACD=\angle ACB+\angle DCB \\ \angle ACD=30^o+35^o \\ \angle ACD=65^o \end{gathered}`

ANSWERS:

(a) The measured angle ACD is 65degrees

(b) The measured angle DCB is 35degrees

(c) The measured angle ACB is 30 degrees