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Q1. Find the measure of an angle. If seven times its complement is less than three Q2. times its supplement. In the given figure, , find the value from a linear pair. If of Q3. In the figure, ray of stands on a line respectively. If bisects . Rays are the angle bisectors . Find Q4. The ray is the ray opposite to Q5. In the figure three coplanar lines intersects in a common point, forming angles as shown. If , then find angles . Q6. In the given figure, . If , show that . is a straight line, find the values of . © Copyright 2011 - 12 Educomp Solutions Ltd. Page 1 of 5 Q7. Two lines intersected a point such that Find all four angles. Q8. Two straight lines bisects Q9. , find . Arm the measure of Q10. intersect each other at point . If and . is produced upto point is the bisector of . Find . In the given figure © Copyright 2011 - 12 Educomp Solutions Ltd. find the value of . Page 2 of 5 Q11. In the given figure, prove that Q12. Q13. If the arms of one angle are respectively parallel to the arms of another angle, show that the two angles are either equal or supplementary. If , find the value of . Q14. In the given figure, the bisector of Q15. In the given figure, divides . meet at in the ratio . Find the and . . Determine the value of . © Copyright 2011 - 12 Educomp Solutions Ltd. Page 3 of 5 Q16. Q17. Q18. Q19. Q20. If the sides of a triangle are produced in order, prove that the sum of the exterior angles so formed is equal to four right angles. If one angle of a triangle is equal to the sum of other two angles, show that the triangle is a right angled triangle. Two angles of triangles are equal and the third angle is greater than each one of them by . Find all the angles. If two straight lines are perpendicular to the same line, prove that they are parallel to each other. If two parallel lines are intersected by a transversal, prove that the bisectors of the two pairs of interior angles enclose a rectangle. Answers A1. A2. A3. A4. A5. Hint: Opposite rays form linear pair of angles. A6. A7. A8. A9. A10. A11. A12. A13. Hint: Prove and (alternate angles and co-interior angles). Then lines parallel to the same line are parallel to each other. Hint: Consider three cases here, Case 1: When both pairs of arms are parallel in same sense, Case2: When both pairs of arms are parallel in opposite sense, Case3: When one air of arms are parallel in same sense and other pair parallel in opposite sense. Use the Alternate interior angles property and corresponding angles property. A14. A15. © Copyright 2011 - 12 Educomp Solutions Ltd. Page 4 of 5 A16. A17. Hint: Produce the sides of the triangle to get the exterior angles, Apply exterior angle property for each of the exterior angles. Add the three equations and apply angle sum property to get the result. Hint: Apply angle sum property to find one of the triangle as . A18. A19. A20. Hint: Use the property that the sum of the interior angles on the same side of the transversal is . Hint: Prove that the figure formed by the bisectors of the two pairs of interior angle is a parallelogram, one of whose angles is . © Copyright 2011 - 12 Educomp Solutions Ltd. Page 5 of 5