Question

In the given figure p is a transversal to lines m and n,angle 1= 60 and angle 2=2/3 of right angle. Prove that mlln​

Answer 1

$\bf\Large{Solution:}$

$\sf{ \angle1 = 60°}$ (given)

According to the property that vertically opposite angles are equal, $\sf{ \angle1= \angle3}$

Thus, $\sf{ \angle3 = 60°}$

Given = $\sf{ \angle2 = 2/3 ×90°= 60°}$

= $\sf{ \angle2= \angle4 }$ (vertically opposite angles)

Thus,

$\sf{ \angle4= 60°}$

$\sf{ \angle4=\angle3 = 60°}$

Converse of alternate interior property - If alternate angles are equal, the lines are parallel. Hence, m||n.

________________________.

Answer 2

Answer:

Solution:

\sf{ \angle1 = 60°}∠1=60° (given)

According to the property that vertically opposite angles are equal, \sf{ \angle1= \angle3}∠1=∠3

Thus, \sf{ \angle3 = 60°}∠3=60°

Given = \sf{ \angle2 = 2/3 ×90°= 60°}∠2=2/3×90°=60°

= \sf{ \angle2= \angle4 }∠2=∠4 (vertically opposite angles)

Thus,

\sf{ \angle4= 60°}∠4=60°

\sf{ \angle4=\angle3 = 60°}∠4=∠3=60°

Converse of alternate interior property - If alternate angles are equal, the lines are parallel. Hence, m||n.