Only top two per cent of people can solve this 'genius' brainteaser

Only the "genius" top two per cent of people can crack this "impossible" problem, according to a mathsprofessor.

A Facebook user, known as "Professor_1o1math" on the social media site, shared the quizand urged his viewers to solve it, before unveiling the correct solution in a video. He penned: "Only 2% of people can solve this. Are you a genius?" The problem starts with a sketch of a small triangle within another larger triangle.

The information available to viewers who want to have a go at solving the problem is that one angle is 20° and another is 80°. In the video, the professor also clarifies that two sides of the triangle are of equal length. The problem dares viewers to determine the size of an angle within the small triangle. In other related news, you'll need a 20/20 vision to stop hidden dogs among sea of cats.

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He states that the solution can be found "using only basic geometry", despite conceding that it can be challenging. To find the correct answer, you'll need to dissect the data available, bear in mind the type of triangles in the image and work out what the solution is. Here, we share the professor's explanation. So if you need more time to find the answer, don't scroll down just yet until you're ready.

Solution

The professor labelled the four angles in the image as A, B, C, D, and explained that the first task is to determine the size of angle B, using the available data - including a triangle with one angle at 20° and another at 80°.

To solve the initial question, the professor stated that angle B would be calculated by subtracting 80° and 20° from 180°, resulting in 80°.

The rationale for the first calculation is that a triangle's angles add up to 180°. Now that we've established that angle B is 80°, and so is angle C, while angle A is 20°, we can conclude that the triangle is isosceles - characterised by two sides of equal length and two identical angles.

The professor then instructed to sketch an equilateral triangle - a triangle where all three sides are of equal length, and all three angles are identical - atop the original triangles. This would also form an additional angle, labelled E, measuring 60°.

The remaining two angles will have the same measurement, totalling 180°. However, with the newly formed equilateral triangle, we can also determine the measurement of the angle adjacent to the 20° angle in the original triangle. Given that the total angle is 60° and the smaller one is 20°, the newly-formed angle will be 40°.

Next, we need to calculate the size of the E, B, C angle, based on the fact that angles B and C are each 80°, and the angle within the equilateral triangle is 60°. To solve for the E, B, C angle, we need to do: 80° - 60° = 20°.

Moving forward, the professor stated we need to draw a line between points C and E, which forms a new triangle - A, C and E. This too is an isosceles triangle, having two sides of equal length.

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Since we previously calculated two of the angles within this triangle to be 60° and 40° respectively, working out the newly-formed angle will be straightforward.

Here's how it works: from the total of 180°, we subtract 40° and then divide the result by two, giving us an answer of 70°. The professor explained that through these calculations, and by sketching the additional triangles, you will have created two congruent triangles.

BYJU'S clarifies that two triangles are considered congruent if their sides are of equal length and their angles are of equal measure. This implies that two triangles can be superimposed side by side and angle to angle.

Continuing his explanation, the professor highlighted two of the triangles in the image - including EBC and BAD - which are identical. He then totalled 80° and 70°, which we previously worked out, and adds up to a total of 150°. This brings us to the solution of the problem, as calculating the smaller angle we were searching for works out like this. From a total of 180°, subtract 150°, and you will have your answer: the smaller angle is 30°.

Did you discover the solution before reading the explanation? Let us know in the comments below.

Geometry is the branch of mathematics concerned with the shape of individual objects, spatial relationships among various objects, and the properties of surrounding space.

Britannica explains geometry is one of the oldest branches of mathematics, having arisen in response to such practical problems as those found in surveying, and its name is derived from Greek words meaning "Earth measurement."