Angle of overlap
Weekly Problem 26 - 2007
The diagram shows two equilateral triangles. What is the value of x?
The diagram shows two equilateral triangles. What is the value of x?
Age
11 to 14
Challenge level
Problem
Image
The diagram shows two equilateral triangles.
What is the value of x?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
Student Solutions
Image
$\angle CBE = (180-75-60)^{\circ} = 45 ^{\circ}$
$\angle DEB= (180-65-60)^{\circ}= 55 ^{\circ}$
$\angle GHB= (45+55)^{\circ} = 100^{\circ}$ (exterior angle of a triangle)
$\angle GHB= (45+55)^{\circ} = 100^{\circ}$ (exterior angle of a triangle)
$\angle HGC = (100-60)^{\circ} = 40^{\circ}$ (exterior angle of a triangle)