Question

Draw a linear pair of angles. Construct angle bisectors of the angles. What type of angle is formed nd how by the bisecting rays?

Answer 1

1) draw in a line BX.
2) Take any radius and place point at A and draw a arc that is cut line BX at C and J.
3) Now place point at C and draw a arc of same radius that cuts our arc at D.
4)Now place point at D and draw a arc of same radius that cuts our arc at E.
5) Join A to E and extended upto F that is our $\angle CAF={120}^{\circ }$
We know that linear angles have sum that form a line and angle of any line is 1${80}^{\circ }$, So linear angles are ${120}^{\circ }is{60}^{\circ }$,
So $\angle BAF={180}^{\circ }-\angle CAF\Rightarrow {60}^{\circ }$
Now for bisecting angle $\angle CAF={120}^{\circ }$ we join line A to point D because D is form by same radius that gives ${120}^{\circ }$ by when we place out point at D so $\angle HAF=\frac{1}{2}\angle BAF\Rightarrow {30}^{\circ }$, here angle disector ray is AG.
So angle from by angle bisectors AH and AG is $\angle HAG$.
therefore $\angle HAG=\angle HAF\Rightarrow {60}^{\circ }+{30}^{\circ }\Rightarrow {90}^{\circ }$