Triangle in a corner
The diagram shows an equilateral triangle touching two straight lines. What is the sum of the four marked angles?
Age
11 to 14
Challenge level
Problem
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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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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 $2\times 180^\circ - 2 \times 60^\circ = 240^\circ$.