Triangle in a Corner
Age
11 to 14
Challenge level
The diagram shows an equilateral triangle touching two straight lines. What is the sum of the four marked angles?
Problem
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The diagram shows an equilateral triangle touching two straight lines.
What is the sum of the four marked angles?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
Student Solutions
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The angles on a straight line add up to $180^\circ$.
Each interior angle of an equilateral triangle is $60^\circ$.
The four marked angles, together with the two interior angles of the equilateral triangle, make two straight lines.
Therefore the marked angles total is $2\times 180^\circ - 2 \times 60^\circ = 240^\circ$.