Question

In the figure, AB = AD , and BD = CD . If angle C measured 19°, what is the measurement ofangle A in degrees?

Answer 1

Given:

`\angle C=19`

If AB=AD then

`\angle ABD=\angle\text{ADB}`

And BD=CD

then:

`\begin{gathered} \angle BCD=\angle DBC \\ \angle C=19 \\ \angle DBC=\angle BCD=190 \end{gathered}`

So:

`\begin{gathered} \angle DBC+\angle BCD+\angle CDB=180 \\ \angle CDB=180-(19+19) \end{gathered}`

From straight line :

`\begin{gathered} \angle CDB+\angle ADB=180 \\ 180-(19+19)+\angle ADB=180 \\ \angle ADB=19+19 \\ =38 \end{gathered}`

and

`\begin{gathered} \angle ADB=\angle ABD \\ \angle ABD=38 \end{gathered}`

For traingle:

`\begin{gathered} \angle DAB+\angle ABD+\angle ADB=180 \\ \angle DAB+38+38=180 \\ \angle DAB=180-(38+38) \\ =180-76 \\ =104 \end{gathered}`