Cho hình thang ABCD(AB//CD).
a) Tính góc A,D biết góc A=2 góc D.
b) Tính góc B,C biết góc B-C=30 độ.
c) Tính góc A,B,D,C biết góc A-D=10 độ, góc B=3 góc C
$\begin{array}{l} \widehat A + \widehat D = {180^0}\\ \Leftrightarrow 2\widehat D + \widehat D = {180^0}\\ \Leftrightarrow \widehat D = {60^0}\\ \Leftrightarrow \widehat A = 2\widehat D = {120^0}\\ Vậy\,\widehat A = {120^0};\widehat D = {60^0}\\ b)\\ \widehat B + \widehat C = {180^0}\\ \widehat B - \widehat C = {30^0}\\ \Leftrightarrow 2.\widehat B = {180^0} + {30^0} = {210^0}\\ \Leftrightarrow \widehat B = {105^0}\\ \Leftrightarrow \widehat C = {105^0} - {30^0} = {75^0}\\ c)\\ \left\{ \begin{array}{l} \widehat A + \widehat D = {180^0}\\ \widehat A - \widehat D = {10^0} \end{array} \right. \Leftrightarrow \left\{ \begin{array}{l} \widehat A = \dfrac{{{{180}^0} + {{10}^0}}}{2} = {95^0}\\ \widehat D = {180^0} - {95^0} = {85^0} \end{array} \right.\\ \left\{ \begin{array}{l} \widehat B + \widehat C = {180^0}\\ \widehat B = 3.\widehat C \end{array} \right. \Leftrightarrow \left\{ \begin{array}{l} 4.\widehat C = {180^0}\\ \widehat B = 3.\widehat C \end{array} \right. \Leftrightarrow \left\{ \begin{array}{l} \widehat C = {45^0}\\ \widehat B = {135^0} \end{array} \right.\\ Vậy\,\widehat A = {95^0};\widehat B = {135^0};\widehat C = {45^0};\widehat D = {85^0} \end{array}$