Question

Find the value of x in each of the following figures if l || m.

Answer 1

$\left(i\right)$Here $\angle HGB=\angle AGE$(vertically opposite angles)

$\angle HGB={110}^{\circ }$

Now, for parallel lines $l$ and $m,$ with transversal $t$.

$\angle HGB+\angle GHD={180}^{\circ }$(Angles on the same side of the transversal are supplementary)

${110}^{\circ }+\angle GHD={180}^{\circ }$

$\angle GHD={180}^{\circ }-{110}^{\circ }={70}^{\circ }$

$\left(ii\right)$For parallel lines $l$ and $m$ with transversal $a$

$\angle AIE=\angle CJI$ (corresponding angles)

$\Rightarrow x={100}^{\circ }$