Answer:
Option C
Yes, they have congruent corresponding angles.
Explanation:
In ΔMNO
Given: [tex]\angle MNO = 105^{\circ}[/tex] , [tex]\angle NMO = 48^{\circ}[/tex]
The sum of measures of these three angles of triangle MNO is 180 degree.
Then;
[tex]\angle MNO + \angle NMO + \angle MON= 180^{\circ}[/tex]
[tex]105^{\circ}+ 48^{\circ} + \angle MON= 180^{\circ}[/tex]
or
[tex]153^{\circ} + \angle MON= 180^{\circ}[/tex]
Simplify:
[tex]\angle MON= 180^{\circ}-153^{\circ}= 27^{\circ}[/tex]
Similarly,
In a given triangle PQR; find angle QPR
[tex]\angle PQR + \angle PRQ + \angle QPR= 180^{\circ}[/tex]
Substitute the value of angles PQR , angle PRQ from the given figure in above equation, we have
[tex]105^{\circ}+ 27^{\circ} + \angle QPR= 180^{\circ}[/tex]
or
[tex]132^{\circ} + \angle QPR= 180^{\circ}[/tex]
Simplify:
[tex]\angle QPR= 180^{\circ}-132^{\circ}= 48^{\circ}[/tex]
Then;
In ΔMNO and ΔPQR
[tex]\angle MNO =\angle PQR = 105^{\circ}[/tex]
[tex]\angle NMO =\angle QPR = 48^{\circ}[/tex]
[tex]\angle MON =\angle PRQ= 27^{\circ}[/tex]
If all pairs of corresponding angles in a pair of triangles are congruent, then the triangles are Similar.
Therefore, ΔMNO[tex]\sim[/tex]ΔPQR .
