Question

find the lettered angle in each case ​

Answer 1

$\huge \bf{Answer} \: \\ \\ \bf{ \angle \: y = 60 \degree} \\ \bf{ \angle \:x = 100 \degree} \\ \\ \huge \bf{Solution} \\ \\ \bf{ABD \: is \: a \: straight \: line \: =180\degree} \\ \\ \bf \: \angle \: y = (180 - 120) \degree \\ \\ \bf{ \angle \: y = 60 \degree} \\ \\ \bf{now} \\ \bf{in \: \triangle \: ABE \: } \\ \\ \bf{\angle \: A + \angle \: B + \angle \: C = 180 \degree} \\ \\ \bf{40 + \angle \: y + \angle \: C = 180 \degree} \\ \\ \bf{\angle \: C = 180 - 100} \\ \\ \bf{ \angle \: C = 80 \degree} \: \\ \\ \bf{therefore} \\ \\ \bf{ACE \: is \: a \: straight \: line = 180 \degree\: } \\ \\ \bf{ \angle \: x + 80 = 180} \\ \\ \bf{ \angle \: x = 100 \degree}$