In the given triangle ABC, DE||BC, and BE bisects $ \angle $DEC. If $ \angle $ACB = 80 degrees, find the value of x.

x = degrees.

Find the unknown angles in the given figure.

Two parallel lines $l$ and $m$ cut by a transversal $t$. If the interior angles of the same side of t be $(2x-8)°$ and $(3x-7)°$, find the measure of each of these angles.

Mohit got an assignment where he had to explain the types of angles formed by a pair of parallel lines.

He completed the assignment but when his teacher checked he saw mistakes. Identify the correct option pointing out the mistake in the parts ( i to iv).$$

In the given figure, $ABCD$ is a quadrilateral in which $AB\parallel DC$ and $AD\parallel BC$.

Prove that $\angle ADC=\angle ABC$.

In the figure (not drawn to scale), $DAE,CBH$ and $ACG$ are straight lines. $DAE\parallel CBH\parallel FG$. Find $x$ and $y$ respectively.

In Figure, if $AB\left|\right|CD$, the value of $x$is

In the figure (not drawn to scale), $AB$ is parallel to $CD$and $\angle ECD$ is a right angle. Find $\angle y.$

Is $ACBD$ in the figure a parallelogram? Why?