Question

How do i solve solve this and explain it to get the correct answer

Answer 1

Notice that angles BDA and CDA lay in the same line

Therefore,

`\begin{gathered} m\angle BDA+m\angle CDA=180 \\ \rightarrow98+m\angle CDA=180 \\ \rightarrow m\angle CDA=180-98 \\ \Rightarrow m\angle CDA=82 \end{gathered}`

Now, since segment AD bisects angle A, we know that angles BAD and DAC are the same, and that

`m\angle A=2\cdot m\angle DAC`

Remember that the sum of the interior angles of a triangle is 180°. This way,

`\begin{gathered} m\angle DCA+m\angle CDA+m\angle DAC=180 \\ \rightarrow69+82+m\angle DAC=180 \\ \rightarrow151+m\angle DAC=180 \\ \rightarrow m\angle DAC=180-151 \\ \Rightarrow m\angle DAC=29 \end{gathered}`

Thereby,

`\begin{gathered} m\angle A=m\angle DAC \\ \rightarrow m\angle A=2\cdot29 \\ \Rightarrow m\angle A=58 \end{gathered}`

Using the fact that the sum of the interior angles of a triangle is 180°, we can state that

`\begin{gathered} m\angle A+m\angle B+m\angle C=180 \\ \rightarrow58+m\angle B+69=180 \\ \rightarrow m\angle B+127=180 \\ \rightarrow m\angle B=180-127 \\ \Rightarrow m\angle B=53 \end{gathered}`

Thereby, we can conclude that angle B measures 53°