#### Chapter 9 Triangle and its Angles R.D. Sharma Solutions for Class 9th MCQ's

**Multiple Choice Questions**

Mark the correct alternative in each of the following:

1. If all the three angles of a triangle are equal, then each one of them is equal to

(a) 90°

(b) 45°

(c) 60°

(d) 30°

**Solution**

2. If two acute angles of a right triangle are equal, then each acute is equal to

(a) 30°

(b) 45°

(c) 60°

(d) 90°

**Solution**

3. An exterior angle of a triangle is equal to 100° and two interior opposite angles are equal. Each of these angles is equal to

(a) 75°

(b) 80°

(c) 40°

(d) 50°

**Solution**

4. If one angle of a triangle is equal to the sum of the other two angles, then the triangle is

(a) an isosceles triangle

(b) an obtuse triangle

(c) an equilateral triangle

(d) a right triangle

**Solution**

5. Side BC of a triangle has been produced to a point D such that ∠ACD = 120°. If ∠B = 1/2 ∠A is equal to:

(a) 80°

(b) 75°

(c) 60°

(d) 90°

**Solution**

(a) 35°

(b) 90°

(c) 70°

(d) 55°

**Solution**

7. In a triangle, an exterior angle at a vertex is 95° and its one of the interior opposite angle is 55°, then the measure of the other interior angle is

(a) 55°

(b) 85°

(c) 40°

(d) 9.0°

**Solution**

8. If the sides of a triangle are produced in order, then the sum of the three exterior angles so formed is

(a) 90°

(b) 180°

(c) 270°

(d) 360°

**Solution**

9. In ΔABC, if ∠A = 100°, AD bisects ∠A and AD ⊥ BC. Then, ∠B =

(a) 50°

(b) 90°

(c) 40°

(d) 100°

**Solution**

10. An exterior angle of a triangle is 108° and its interior opposite angles are in the ratio 4 : 5. The angles of the triangle are

(a) 48°, 60°, 72°

(b) 50°, 60°, 70°

(c) 52°, 56°, 72°

(d) 42°, 60°, 76°

**Solution**

11. In a Δ

*ABC*, if ∠

*A*= 60°, ∠

*B*= 80° and the bisectors of ∠

*B*and ∠

*C*meet at

*O*, then ∠

*BOC*=

(a) 60°

(b) 120°

(c) 150°

(d) 30°

**Solution**

(a) 45°

(b) 95°

(c) 135°

(d) 90°

**Solution**

13. Line segments AB and CD intersect at O such that AC || DB. If ∠CAB = 45° and ∠CDB = 55°, then ∠BOD =

(a) 100°

(b) 80°

(c) 90°

(d) 135°

**Solution**

(a) 90° + x°/2

(b) 90° - x°/2

(c) 180° + x°/2

(d) 180° - x°/2

**Solution**

(a) 25°

(b) 50°

(c) 100°

(d) 75°

**Solution**

16. The side BC of ΔABC is produced to a point D. The bisector of ∠A meets side BC in L. If ∠ACD = 115°, then ∠ALC=

(a) 85°

(b) (72 ½)°

(c) 145°

(d) none of these

**Solution**

17. In Fig. 943, if EC∥AB, ∠ECD = 70° and ∠BDO = 20° and , then ∠OBD is

(a) 20°

(b) 20°

(c) 20°

(d) 70

**Solution**

18. In Fig. 9.44,

*x*+

*y*=

(a) 270

(b) 230

(c) 210

(d) 190°

**Solution**

19. If the measures of angles of a triangle are in the ratio of 3 : 4 : 5, what is the measure of the smallest angle of the triangle?

(a) 25°

(b) 30°

(c) 45°

(d) 60°

**Solution**

20. In Fig. 9.45 if AB⟂BC, then x =

(a) 18

(b) 22

(c) 25

(d) 32

**Solution**

21. In Fig 9.46, what is z in terms of x and y?

(a) x + y + 180

(b) x + y − 180

(c) 180° − (x + y)

(d) x + y + 360°

**Solution**

(a) 37

(b) 43

(c) 45

(d) 47

**Solution**

23. In Fig. 9.48, what is y in terms of x?

(a) 3/2 x

(b) 4/3 x

(c) x

(d) 3/4 x

**Solution**

24. In Fig. .49, if l1∥l2, the value of x is:

(a) 22½

(b) 30

(c) 45

(d) 60

**Solution**

25 . In Fig. 9.50, what is the value of x?

(a) 35

(b) 45

(c) 50

(d) 60

**Solution**

26. In △RST (See Fig. 9.51), what is the value of x?

(a) 40

(b) 0

(c) 80

(d) 100

**Solution**

27. In Fig. 9.52, the value of x is

(a) 65

(b) 80

(c) 95

(d) 120

**Solution**

28. In Fig. 9.53, if BP∥CQ and AC=BC, then the measures of x is:

(a) 20

(b) 25

(c) 30

**Solution**

29. In Fig. 9.54, AB and CD are parallel lines and transversal EF intersects at P and Q respectively.

If ∠APR = 25, ∠RQC = 30 and ∠CQF = 65, then

(a) x = 55, y = 40

(b) x = 50, y = 45

(c) x = 60, y = 35

(d) x = 35, y = 60

**Solution**

30. The base BC of triangle ABC is produced both ways and the measure of exterior angles formed are 94° and 126°. Then, ∠BAC =

(a) 94°

(b) 54°

(c) 40°

(d) 44°

**Solution**

In the given problem, the exterior angles obtained on producing the base of a triangle both ways are 94 and 126. So, let us draw ΔABC and extend the base BC, such that:

∠ACD = 126

∠ABE = 94

Now, since BCD is a straight line, using the property, “angles forming a linear pair are supplementary”, we get

∠ACB + ∠ACD = 180

⇒ ∠ACB + 126 = 180

⇒ ∠ACB = 180 - 126

⇒ ∠ACB = 54

Similarly, EBS is a straight line, so we get,

∠ABC + ∠ABE = 180

⇒ ∠ABC + 94 = 180

⇒ ∠ABC = 180 - 94

⇒ ∠ABC = 86

Further, using angle sum property in ΔABC

∠ABC + ∠ACB + ∠BAC = 180

⇒ 54 + 86 + ∠BAC = 180

⇒ ∠BAC = 180 - 140

⇒ ∠BAC = 40

Thus, ∠BAC = 40

Therefore, the correct option is (c).