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Question

Mathematics Question on Angle Sum Property Of A Triangle

Find the value of the unknown x in the following diagrams:
list of diagrams

Answer

The sum of all interior angles of a triangle is 180°180°. By using this property, these problems can be solved as follows.

(i) x+50°+60°x + 50° + 60°
= 180°x+110°=180°x180° x + 110° = 180° x
= 180°−110°=70°180° -110° = 70°

(ii) x+90°+30°x + 90° +30°
= 180°x+120°180° x + 120° =180°x180° x
= 180°−120°180° - 120°
=60°60°

(iii) x+30°+110°=180°x+140°=180°x + 30° + 110° =180° x + 140° = 180°
x=180°−140°=40°x = 180° - 140° = 40°

(iv) 50°+x+x=180°50° + x + x = 180°
50°+2x=180°50° + 2x = 180°
2x=180°−50°=130°2x = 180° - 50° = 130°
x=130∘2=65∘x= \frac{130\degree}{2}=65\degree

(v) x+x+x=180°x + x + x = 180°
3x=180°3x = 180°
x=1803=60∘x=\frac{180}{3}=60\degree

(vi) x+2x+90°=180°x + 2x + 90° = 180°
3x=180°−90°=90º3x = 180° - 90° = 90 º
x=90∘3=30∘x = \frac{90\degree}{3}=30\degree