Question
In Fig., it being given that $\angle1 = 65^\circ,$ find all the other angles.
✓
Answer
Given,
$\angle1=\angle3 $ are the vertically opposite angles
Therefore, $\angle3 = 65^\circ$
Here, $\angle1 + \angle2 = 180^\circ$ are the linear pair
Therefore, $\angle2 = 180^\circ-65^\circ$
$= 115^\circ$
$\angle2 = \angle4$ are the vertically opposite angles
Therefore, $\angle2 = \angle4 = 115^\circ$
And $\angle3 = 65^\circ$
$\angle1=\angle3 $ are the vertically opposite angles
Therefore, $\angle3 = 65^\circ$
Here, $\angle1 + \angle2 = 180^\circ$ are the linear pair
Therefore, $\angle2 = 180^\circ-65^\circ$
$= 115^\circ$
$\angle2 = \angle4$ are the vertically opposite angles
Therefore, $\angle2 = \angle4 = 115^\circ$
And $\angle3 = 65^\circ$
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