In figure 16.1 4 determine angle p + angle q + angle r + angle s + angle t
Dear Student,
Angle P = 180 - Angle 5 -Angle 10( Where Angle 5 and Angle 10 are the exterior angles of the pentagon)
Similarly, we can conclude that,
Angle P+Angle Q+ Angle R+ Angle S + Angle T = (180*5) - (Angle 1+ Angle 2+Angle 3+........ +Angle 10)
Now each interior angle of a pentagon = (n-2)*180/n (where n=5)
Therefore here, each interior angle = 3*180/5 = 108.
Exterior angles and interior angles form a linear pair. Thus exterior angle = 180-108 = 72.
Now, All Angles 1 to 10 are 72 each.
Thus, Angle P+Angle Q+ Angle R+ Angle S + Angle T = 900 - 10*72 = 900-720 = 180 degrees.
Thus the required answer is 180 degrees.
Regards.
Angle P = 180 - Angle 5 -Angle 10( Where Angle 5 and Angle 10 are the exterior angles of the pentagon)
Similarly, we can conclude that,
Angle P+Angle Q+ Angle R+ Angle S + Angle T = (180*5) - (Angle 1+ Angle 2+Angle 3+........ +Angle 10)
Now each interior angle of a pentagon = (n-2)*180/n (where n=5)
Therefore here, each interior angle = 3*180/5 = 108.
Exterior angles and interior angles form a linear pair. Thus exterior angle = 180-108 = 72.
Now, All Angles 1 to 10 are 72 each.
Thus, Angle P+Angle Q+ Angle R+ Angle S + Angle T = 900 - 10*72 = 900-720 = 180 degrees.
Thus the required answer is 180 degrees.
Regards.