Triangle Angle Sum & Properties
Explore the concept of the angle sum in a triangle, types of triangles based on sides and angles, properties of triangles, and how to calculate unknown angles in different types of triangles with helpful examples. Understanding these fundamental principles in geometry is essential for math enthusiasts and students.
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Presentation Transcript
03 July 2025 Angle sum in a triangle LO: To know that the sum of the angles in a triangle is 180 . www.mathssupport.org
Types of triangles A triangle is a polygon which has three sides. According to the sides the triangles could be: Equilateral triangle triangle Isosceles Scalene triangle 3 equal sides 3 equal angles 2 equal sides 2 equal angles no equal sides no equal angles www.mathssupport.org
Types of triangles According to the angles the triangles could be: Right-angled triangle triangle Acute-angled Obtuse-angled triangle It contains one 90o angle And two acute angles. It contains an obtuse angle And two acute angles. All angles are acute www.mathssupport.org
The sum of the angles in any triangle Take 3 identical copies of a triangle like so: b b b c a c a c a Colour the corresponding angles the same colour in each triangle. Draw a straight line. Stick the triangles on your book like this. b c a What can you say about the angles a, b and c? They are the three angles of a triangle What do they add up to? 180 a + b + c = www.mathssupport.org
Types of triangles Other properties of triangles: is opposite to the largest angle The longest side Any exterior angle is equal to the sum of the interior opposite angles www.mathssupport.org
Calculating unknown Angles Example 1 Calculate angle a. 65o a The angles in the triangle add up to 180 Since it is a right angled-triangle, one angle is 90 The two acute angles in a right-angled triangle add up to 90 a + 65 = 90 a = 90 65 a = 25o www.mathssupport.org
Calculating unknown Angles Example 2 Calculate angles a, b and c b a c The triangle is equilateral, a = b = c Therefore, to find the size of one angle ? =180 3 a = 60 = b = c www.mathssupport.org
Calculating unknown Angles Example 3 Calculate angle A and angle B. To calculate angle A. The triangle is isosceles, so angles opposite to equal sides are equal. A = C A = 65 To calculate angle B. B C= 65o A A + B + C= 180 65 + B + 65= 180 130 + B = 180 B= 50o www.mathssupport.org
Calculating unknown Angles Calculate angles x and y Example 4 75o 40o y x To calculate angle x. To calculate angle y. x and y are supplementary angles, so, they add up to 180 The sum of the angles in a triangle is 180 x + 75 + 40= 180 x + y= 180 65 + y = 180 y= 115o 115 + x = 180 x= 65o www.mathssupport.org
Calculating unknown Angles Example 5 Find the values of the variable. To calculate value of x. 2x + (x + 20) + x= 180 2x 4x + 20= 180 4x = 160 (x + 20)o xo x= 40o www.mathssupport.org
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