Triangle sum property.

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Presentation transcript:

Triangle sum property

Triangle Sum Property Theorem The sum of the measures of the interior angles of a triangle is 180o. 3 2 1 ∠1 + ∠2 + ∠3 = 180°

60º 90º 30º 180º Property of triangles Can we draw a triangle with angles 600, 900 and 300 We know that the sum of the measures of the interior angles of a triangle is 180o. Sum of 3 angles are 60º 90º Since sum of 3 angles is equal to 180, triangle can be formed using the given angles. 30º + 180º

70º 70º 70º 210º Property of triangles Can we draw a triangle with angles 700, 700 and 700 We know that the sum of the measures of the interior angles of a triangle is 180o. Sum of 3 angles are 70º Since sum of 3 angles is not equal to 180, triangle cannot be formed using the given angles. 70º 70º + 210º

What is the missing angle? We know that the sum of angles in a triangle is 180º Missing angle = 180 - sum of other two angle Missing angle = 180º - 140º = 40º Sum of other two angle is 70º ? 70º + 70º 140º 70º

90º 30º ? 120º 30º 90º What is the missing angle? + We know that the sum of angles in a triangle is 180º Missing angle = 180 - sum of other two angle Missing angle = 180º - 120º = 60º Sum of other two angle is 90º 30º 90º ? + 30º 120º

Find all the angle measures Solution We know that sum of angles in a triangle is 180 35x + 45x + 10x = 180 90x = 180 (dividing 90 on both sides) 45x 10x 35x Angle 1 = 35x = 35 x 2 =70 Angle 2 = 45x = 45 x 2 =90 Angle 3 = 10x = 10 x 2 =20 Ans:- The three angles are 700 , 900 , 200

Find the missing angles. Solution We know that sum of angles in a triangle is 180 2x + x + 90 = 180 2x + x + 90 - 90 = 180 - 90 (subtracting 90 on both sides) 2x + x = 90 3x = 90 (dividing 3 on both sides) x = 30 Angle 1 = 2x = 2 x 30 =60 Angle 2 = x = 30 Ans:- The three angles are 600 , 300 , 900

Three angles of a triangle are xº, x+10º and x+20º, Find x Solution We know that sum of angles in a triangle is 180 x + (x + 10) + (x + 20) = 180 x + x + x + 10 + 20 = 180 3x + 30 = 180 3x + 30 - 30 = 180 - 30 (subtracting 30 on both sides) 3x =150 (dividing 3 on both sides) x = 50

Try These: Can we draw a triangle using the given angles? 80O , 60O , 70O Find the third angle, given two angles of triangle: 50O , 90O Find the value of x, if three angles of a triangle are 2x, 3x, x