Question

In the given figure DE || BC. If ZADF = 130° and C = 50°, then find
(ii) ABC
(i) ADE
(iii) DEC
Give reasons.​

Answer 1

$\large{\texttt{Given :-}}$

$\texttt{DE||BC}$

$\mathtt{\angle ADF = 130°}$

$\mathtt{\angle C = 50°}$

$\large{\texttt{To find :-}}$

$\mathtt{\angle ADE = ?}$

$\mathtt{\angle ABC = ?}$

$\mathtt{\angle DEC = ?}$

$\large{\texttt{Solⁿ :-}}$

$\mathtt{\angle ADE = 180°- \angle ADF \;\;\;\;\;\; [linear \; pair]}$

$\;\;\;\;\;\;\;\;\;\; \mathtt{ = 180°-130° = 50°}$

$\mathtt{\angle ABC = \angle ADE = 50° \;\;\;\;\;\;\; [corres. \; \angle s ]}$

$\mathtt{\angle DEC = 180°- \angle ACB \;\;\;\;\;\; [co-int \; \angle s]}$

$\mathtt{\;\;\;\;\;\;\;\;\; = 180°-50° = 130°}$