triangles solution

Solutions triangles

Fill in the blanks

1.     Less than

2.     More than

3.     180^o

4.     Acute

5.     Obtuse

6.     60^o

Which triangles are feasibles

1.     6+1=7

The sum of two smaller side equal to third therefore it cannot be a triangle (Sum of two angles are always more than third side)

2.     3+2=5

5<6

The sum of two smaller side less than third therefore it cannot be a triangle (Sum of two angles are always more than third side)

3.     80+70+40= 190

Sum of three angles is not equal to 180^o. Therefore it cannot be a triangle.

4.     170+6+4=180

    Sum of three angles is equal to 180^o. Therefore it is a triangle.

Solve

1.     Right angle = 90

Given angle=30

90+30+ 3^rd angle=180

120+ 3^rd angle=180

3^rd angle= 180-120

3^rd angle = 60

2.     One of the equal angles =40

∠A+∠B+∠C=180

40+40+∠C=180

80+∠C=180

∠C=180-80

∠C=100

3.     Unequal angle of isosceles triangle=30

∠A+∠B+∠C=180

30+∠B+∠C=180

∠B+∠C=180-30

∠B+∠C=150

∠B=∠C=150/2

∠B=∠C=75

4.     ∠A+∠B+∠C=180

80+20+∠C=180

100+∠C=180

∠C=180-100

∠C=80

5.     Right angle= 90

Isosceles triangle= two other angles are equal

∠A+∠B+∠C=180

90+∠B+∠C=180

∠B+∠C=180-90

∠B+∠C=90

∠B=∠C=90/2

∠B=∠C=45

6.   

   

No of triangles= 32

Different ways in which the marked angle can be named:

∠ACE, ∠ACJ, ∠ACI

∠GCE, ∠GCJ, ∠GCI

∠HCI, ∠HCJ, ∠HCE

∠ICH, ∠ICG, ∠ICA

∠JCH, ∠JCG, ∠JCA

∠ECH, ∠ECG, ∠ECA

7. vertices- A, B, C

Sides- AB, BC, CA

Acute angles- ∠ABC, ∠ACB

Obtuse angles- ∠BAC