Video: KS2-M17 • Paper 3 • Question 13

Circle the pentagon with exactly four acute angles.

03:07

Video Transcript

Circle the pentagon with exactly four acute angles.

There are two things we need to know to help us answer this question. The first is, what is a pentagon? A pentagon is a 2D shape which has five sides. So let’s check first of all which of these shapes are pentagons.

The first shape is a pentagon. It has five sides. In fact, this pentagon could be called a regular pentagon because each of its sides are equal in length. So the angles in this pentagon are also equal in size. The second shape is also a pentagon. And you may’ve noticed that it has two right angles. The third shape is also a pentagon. And we can mark each of its angles as shown.

This shape is a hexagon because it has six sides. We can eliminate this shape because we’re looking for a pentagon with four acute angles. And the final shape is also a hexagon because it has six sides. We can call this one a regular hexagon because each of its sides is equal in length. But we’re not looking for a hexagon. We’re looking for a pentagon.

Now that we’ve identified all of the pentagons, we need to find the one which has four acute angles. An acute angle is an angle which measures less than 90 degrees. We can eliminate the first pentagon, which is a regular pentagon, because all of its angles are equal.

Remember, the question asks us to find a pentagon with four acute angles. We can also eliminate the second pentagon because two of its angles are right angles, which only leaves three angles left. So we’re guessing that the third pentagon is the one with four acute angles. By drawing a right angle onto each of the four smaller angles, we can see that each of them is less than 90 degrees. And this angle is more than 90 degrees.

Finally, the question asks us to circle the pentagon with exactly four acute angles. To find the answer, first we identified all of the pentagons. Then we looked closely at each pentagon’s angles, then circled the pentagon with exactly four acute angles.

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