8. In the figure, two straight lines PQ and Rintersect each other at O. If POT = 75°, findtbvalues of a, b and c.ar2cn s1sne4b°Cl75bo

8. In the figure, two straight lines PQ and Rintersect each other at O

1.	8. In the figure, two straight lines PQ and Rintersect each other at O. If POT = 75°, findtbvalues of a, b and c.ar2cn s1sne4b°Cl75bo
Answer» We have two straight lines PQ and RS.And,∠ POT = 75°So,∠ POR +∠ POT +∠ TOS = 180° (Linear pair angles)Now substitute the given values, we get4b + 75° + b = 180°5b = 75° = 180°5b = 180° - 75°5b = 105°b = 21°And,∠ POR = 4b = 4 (21)∠ POR = 84°And,∠ SOQ =∠ POR (vertically opposite angles)Substitute the values, we geta = 84°And,∠ QOR =∠ POS (vertically opposite angles)Substitute the values, we get2c = 75° + 21°2c = 96°c = 96/2c = 48°So,a = 84°b = 21°c = 48°