Question

Answer 1

a. \(A-D=30^0\Rightarrow A=D+30^0\)

\(B+C=4D\Rightarrow A+B+C=D+30^0+4D\)

\(\Rightarrow A+B+C=5D+30^0\)

\(\Rightarrow A+B+C+D=6D+30^0\)

\(\Rightarrow6D+30^0=360^0\)

\(\Rightarrow D=55^0\)

\(\Rightarrow A=D+30^0=85^0\)

b.

Do ABCD là hình thang \(\Rightarrow A+D=180^0\)

\(\Rightarrow2D+D=180^0\)

\(\Rightarrow3D=180^0\Rightarrow D=60^0\) \(\Rightarrow A=2D=120^0\)

Do hình thang cân nên: \(\left\{{}\begin{matrix}B=A=120^0\\C=D=60^0\end{matrix}\right.\)