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Given : A triangle ABC.To Prove:∠A + ∠B + ∠C= 180^{0}Construction: Draw CE such that CE || AB |

1)BA || CE | 1) By Construction |

2) ∠A = ∠ACE | 2) Alternate interior angle |

3) ∠B = ∠DCE | 3) Corresponding angles |

4)∠A + ∠B = ∠ACE + ∠DCE | 4) Addition property of (1) and (2) |

5) ∠A + ∠B + ∠ACB = ∠ACE + ∠DCE + ∠ACB | 5) Adding ∠ACB to both sides |

6) ∠A + ∠B + ∠C = 180^{0} |
6) Straight line angles. |

1) Two angles of a triangle are of measures 75

Let ABC be a triangle such that ∠B = 75

By angle sum property of triangles,

∠A + ∠B + ∠C = 180

∠A + 75 + 35 = 180

∠A + 110 = 180

∠A = 180 -110

∠A = 70

2) Of the three angles of a triangle, one is twice the smallest and another is three times the smallest. Find the angles.

Let the smallest angle be x ,

Other two angles be 2x and 3x.

By angle sum property,

x + 2x + 3x = 180

6x = 180

x = 180/6

x = 30

2x = 2 (30) = 60

3x = 3(30) = 90

So, the three angles are 30

3) If the angles of a triangle are in the ratio 2:3:4, determine the three angles.

Let the ratio be x .

So, the angles are 2x, 3x and 4x.

By angle sum property,

2x + 3x + 4x =180

9x = 180

x = 180/9

x = 20

three angles are 2x = 2(20) = 40

3x = 3(20) = 60

4x = 4(20) = 80

• Introduction to Triangles

• Types of Triangles on the basis of Sides

• Types of Triangles on the basis of Angles

• Angle Sum Property of Triangles

• Exterior and Interior angles of Triangle

• Triangle Inequality Property

• Congruent Triangles

• Postulates of Congruent Triangle

• Inequality in Triangle

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