Fangs
Weekly Problem 7 - 2013
Three of the angles in this diagram all have size $x$. What is the value of $x$?
Three of the angles in this diagram all have size $x$. What is the value of $x$?
Age
11 to 14
Challenge level
Problem
What is the value of $x$ in this diagram?
If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.
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If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.
Student Solutions
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Alternate angles BDF and DFG are equal, so lines BD and FG are parallel.
Therefore angle BCA = angle FGC = $80^{\circ}$ (corresponding angles).
Consider triangle ABC: $x + 70 + 80 = 180$ so $x=30$.
Alternatively, note that angle ACB = angle DCE, and therefore triangles ABC and CDE are similar, so angle DEC = $70^{\circ}$. Similarly, angle DCE is $80^{\circ}$, and therefore $x=30^{\circ}$.