Question

Activity-
(1)In the figure below, there is a pair of parallel lines and a third line cutting across them. In the figure, a measure of one angle is given and another angle is marked. Find out its measure and write it in the figure itself. (2 marks)

(2) In the figure below, there is a pair of parallel lines and a third line cutting across them. In the figure, a measure of one angle is given and another angle is marked. Find out its measure and write it in the figure itself.

Answer 1

(1)Here, $\angle DFG={60}^{\circ }$ (Given)
So, $\angle DBC={60}^{\circ }$ [Since parallel lines (AC and EG) make equal angles with any other line (DH)]
$\therefore \angle ABH={60}^{\circ }$ [Among the four angles made by two lines cutting across each other, each pair of opposite angles are equal]
Hence, the required angle $=\angle ABH={60}^{\circ }$
(2) Let's label the given figure as follows;
Here, $\angle CBH={120}^{\circ }$ (Given)
So, $\angle GFH={120}^{\circ }$ [Since parallel lines (AC and $EG$ ) make equal angles with any other line (DH)] Hence, the required angle $=\angle GFH={120}^{\circ }$