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

GMAT

GRE

1st Grade

2nd Grade

3rd Grade

4th Grade

5th Grade

6th Grade

7th grade math

8th grade math

9th grade math

10th grade math

11th grade math

Precalculus

Worksheets

Chapter wise Test

MCQ's

Math Dictionary

Graph Dictionary

Multiplicative tables

Math Teasers

NTSE

Chinese Numbers

CBSE Sample Papers