LINE AND ANGLE

LINE AND ANGLES

1.       In an obtuse-angled triangle ABC, A is the obtuse angle and O is the orthocenter. If BOC = 54⁰, then BAC is

(1) 108⁰                         (2) 126⁰                      (3) 136⁰                      (4) 116⁰

2.       If I is the in-centre of ABC and A = 60⁰, then the value of BIC is

(1) 100⁰                         (2) 120⁰                      (3) 150⁰                      (4) 116⁰

3.       If a straight line L makes an angle θ (θ ˃ 90⁰) with the positive direction of x-axis, then the acute angle made by a straight line L₁, perpendicular to L, with the y-axis is

(1)  + θ                       (2)  - θ                       (3) π + θ                      (4) π – θ

4.       A, O, B are three points on a line segment and C is a point not lying on AOB. If AOC = 40⁰ and OX, OY are the internal and external bisectors of AOC respectively, then BOY is

(1) 70⁰                          (2) 80⁰                         (3) 72⁰                         (4) 68⁰

5.       The side BC of ABC is produced to D. If ACD = 108⁰ and B =  A , then A is

(1) 36⁰                          (2) 72⁰                         (3) 108⁰                       (4) 59⁰

6.       If in any triangle ABC, the base BC is produced in both ways, the sum of the exterior angles at B and C is

(1)  π – A                     (2)  π + A                    (3)  + A                     (4)  – A

7.       In the figure below, lines k and l are parallel. The value of a^o + b^o is

(1) 45⁰                         (2) 100⁰                       (3) 180⁰                       (4) 360⁰

8.       In the figure below, if AB || CD and CE perpendicular ED, then the value of x is

(1) 53                           (2) 63                          (3) 37                           (4) 45

9.       The sum of the internal angles of a regular polygon is 1440⁰. The number of sides is

(1) 8                             (2) 10                           (3) 12                          (4) 6

10.   The point of intersection of the diagonals AC and BD of the cyclic quadrilateral ABCD is P. If APB = 64⁰ and CBD = 28⁰, the measure of ADB is

(1) 32⁰                         (2) 36⁰                          (3) 56⁰                         (4) 28⁰

11.   In ABC, AB = AC, O is a point on BC such that BO = CO and OD is perpendicular to AB and OE is perpendicular to AC. If BOD = 30⁰, then measure of AOE is

(1) 45⁰                         (2) 60⁰                          (3) 75⁰                         (4) 30⁰

12.   In ABC, BAC = 90⁰ and AD perpendicular BC. If BD = 3cm and CD = 4cm, then the length of AD is

(1) 3.5cm                   (2) 5cm                        (3) 2 cm                 (4) 6cm

13.   The interior angle of a regular polygon exceeds its exterior angle by 108⁰. The number of the sides of the polygon is

(1) 12                          (2) 16                           (3) 14                          (4) 10

14.   The measure of an angle whose supplement is three times as large as its complement is

(1) 75⁰                        (2) 30⁰                          (3) 45⁰                         (4) 60⁰

15.   If two supplementary angles differ by 44⁰, then one of the angles is

(1) 68⁰                                   (2) 65⁰                            (3) 102⁰                      (4) 72⁰

16.   The measure of two angles of a triangle are in the ratio 4 : 5. If the sum of these two measures is equal to the measure of the third angle, find the smallest angle

(1) 10⁰                        (2) 50⁰                           (3) 90⁰                        (4) 40⁰

17.   If the three angles of a triangle are :

(x + 15⁰), ( + 6⁰) and ( + 30⁰) , then the triangle is

(1) isosceles              (2) right angled          (3) equilateral           (4) scalene

18.   Internal bisectors of Q and R of PQR intersect at O. If BAC = 40⁰ and ABC = 65⁰ , then CED is :

(1) 36⁰                                     (2) 24⁰                          (3) 12⁰                          (4) 6⁰

19.   In ABC, D and E are two mid points of sides AB and AC respectively. If BAC = 40⁰, ABC = 65⁰, then CED is equal to

(1) 130⁰                       (2) 75⁰                        (3) 125⁰                        (4) 105⁰

20.   O is the circumcentre of ABC. If BAC = 85⁰, BCA = 75⁰, then OAC is equal to

(1) 60⁰                         (2) 70⁰                           (3) 50⁰                          (4) 40⁰

21.   O is the incentre of PQR and QPR = 50⁰, then the measure of QOR is

(1) 125⁰                       (2) 100⁰                        (3) 130⁰                        (4) 115⁰

22.   The internal bisectors of the B and C of the ABC, interaction at O. If A = 100⁰, then the measure of BOC is

(1) 140⁰                       (2) 120⁰                        (3) 110⁰                        (4) 130⁰